UNIVERSITY OF LONDON

ATTENUATION OF SOUND IN GAS MIXTURES

THESIS SUBMITTED FOR THE PH.D. DEGREE IN THE FACULTY OF SCIENCE

BY

RONALD KITCHING

JUNE 1963.

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ABSTRACT.

The attenuation of sound waves in gas contained in a tube has been measured for air, oxygen and water vapour-oxygen mixtures at frequencies between 90 and 1,200 cycle. sec.~l The magnitude of the Helmholtz-Kirchhoff coefficient has been determined for air contained in a smooth walled duralumin tube. The variation of the absorption with frequency and moisture content has been investigated for oxygen.

The tube was terminated at one end by a fixed reflector and at the other by a plane diaphragm producing the sound waves. The impedance of the diaphragm-gas column system was investigated near the natural modes of the tube and analysed by means of a circle diagram to yield the attenuation coefficient.

The magnitude of the Helmholtz-Kirchhoff coefficient with an air filled tube was found to be 15.3^ higher than the theoretical value. The relaxation absorption in oxygen-water vapour mixtures was found to be in general agreement with the theory of Kneser. The value of the vibrational specific heat for oxygen was found to be (0.0332 =h 0.0015)H. The frequency of maximum absorption was found to be a quadratic function of the water vapour c one entrât ion.

CONTENTS.

Chapter PageABSTRACT. 2

1 INTRODUCTION. 92 . THE THEORY OF THE RELAXATION EFFECT. 163 THE THEORY OF THE METHOD. 244 THE RESONANCE TUBE, REFLECTOR AND LOUDSPEAKER. 39

(a) The Resonance Tube. 39(b) The Reflector. 43(c) The Loudspeaker. 43(d) The Optical System. 52

5 TEMPERATURE CONTROL AND MEASUREMENT. 55(a) Temperature Control. 55(b) Temperature Measurement. 62

6 FREQUENCY MEASUREMENT. 637 IMPEDANCE MEASUREMENT. 738 HUMIDITY MEASUREMENT. 77

9 GAS PREPARATION AND PURIFICATION. 81(a) Air. 81(b) Oxygen. 82

10 RESULTS AND DISCUSSION. 87(a) Air. 87(b) Oxygen. 92

Chapter Page11 DISCUSSION OF THE METHOD. 109

APPENDIX. EXPERIMENTAL PROCEDURE AND SPECIMEN H ICALCULATION.

REFERENCES. 120

FIGURES.

Figure Page1 Graph showing the frequency of maximum 14

absorption against water vapour/oxygen molecular concentration for oxygen gas.

2 Graph of the relaxation absorption 23coefficient per wavelengthjlx. againstthe angular frequency iJ.

3 The Argand diagram. 284 Graph of the impedance of the diaphragm- 28

gas column system against frequency(reactance of positive).

5 The practical circle diagram (reactance 31

of Z q positive).6 Graph of tan <f> against frequency. 317 To shav the effect of the Zg estimate 34

upon the tan (j> against frequency graph.8 Graph of the impedance of the diaphragm- 36

gas column system against frequency(reactance of Z^ negative).

9 The practical circle diagram (reactance 35

of Zg negative).10 The reflector. 44

11 The loudspeaker. 45

Figure Page12 The diaphragm. 4813 The lens mount. 4814 Graph of the amplitude of vibration of the 51

diaphragm against the moving coil current.15 The optical system. 5316 The thermostat tank. 5617 Circulation of water in the thermostat tank. 57

18 Electrical heater connections in the thermostat 57tank.

19 The thermistor mount. 5720 The circuit diagram of the thermistor 60

temperature controller.21 Graph of the frequency stability of the 65

Airmec oscillator.22 Graph of the frequency stability of the 66

Philips RC oscillator.23 The circuit diagram of the amplifier for the 67

Airmec oscillator.24 The circuit diagram of the amplifier for the 68

Philips RC oscillator.25 The camera box. 70

25 The flash tube circuit. 7027 Specimen photograph of the revolution counters. 7228 Measurement of the current through the moving 74

Figure Pagecoil.

29 Calibration graph of the galvanometer thermal 75scale.

30 The side tube for introducing distilled water 79into the resonance tube.

31 The gas purifying system. 8332 Graph of against f for air. 9033 Graph of absorption coefficient against 102

Water vapour/oxygen molecular ratio at 98 c/s.34 " 196 c/s. 10235 " 294 c/s. 10335 * 598 o/s. 10337 " 894 c/s. 10438 * 1,190 o/s. 10439 Graph of the maximum value of the relaxation 105

absorption against frequency.40 Graph of frequency of maximum absorption 107

against water vapour/oxygen molecular ratiofor oxygen gas.

41 Specimen impedance plot 13/10/61. H 5

42 Specimen circle diagram 13/10/61. 117

43 Specimen tan (j> against frequency graph 13/10/61. 113

8

TABLES

Table Page1 Internai diameter of the resonance tube. 402 Length of the resonance tube. 423 Results obtained for the absorption

coefficient of air.88

4 Comparison of the present result for the difference between the experimental and theoretical values of the Helmholtz-

93

Kirchhoff coefficient with the resultsobtained by other workers.

5 Results obtained for the absorption coefficient 94of oxygen at 98 c/s.

6 196 c/8. 957 » 294 c/s. 968 îf 598 c/s. 979 tè 894 c/s. 9810 t» 1,190 c/s. 9911 Specimen observations 13/10/61. 115

CHAPTER 1

INTRODUCTION.

The classical theory of absorption of sound in gases arising from viscosity and heat conduction was given by Stokes (1) and Klrchhoff (2). When the gas is enclosed in a tube the velocity and attenuation are given by

I —

where is the velocity of sound in in a tube of radius r,

s enclosed

C is the velocity of sound in the free gas,u n jT*is the attenuation coefficient per cm. in

gas enclosed in a tube of radius r,"P is the frequency of the sound wave,P is the Helmholtz-Kirchhoff coefficient

which is a function of the viscous and thermal properties of the gas.

Jeans (4) and Herzfeld and Rice (5) developed the theory of thermal relaxation for polyatomic gases.The energy of a molecule depends upon the number of

degrees of freedom possessed by that molecule. A monatomic

10

gas has three translational degrees of freedom, a diatomic gas has these three plus two of rotation and two of vibration and a polyatomic gas may have many more. The translational degrees of freedom are usually referred to as the external or primary degrees of freedom and the vibrational and rotational as the internal or secondary degrees of freedom. The passage of a sound wave causes compressions and rarefactions which change the energy of the external degrees of freedom. The redistribution of energy between the external and internal degrees of freedom then occurs with a time constant called the relaxation time. The delay in adjustment to the new conditions is due to the fact that the redistribution of energy between the degrees of freedom takes place in collisions with other molecules. The redistribution of energy between translational and rotational degrees of freedom is effected after a few collision mean periods which corresponds to a relaxation time IT of about 10~^secs. However the redistribution of energy between translational and vibrational degrees of freedom is a much slower process and T is considerably larger.

The period of the sound wave passing through the gas is very important in determining the magnitude of the absorption of the wave. If the period of the sound wave is considerably greater than the time taken to establish equilibrium, little energy is lost because the gas is in equilibrium at any Instant. If the period of

11the sound wave is considerably less than the time taken to establish equilibrium, very little energy is transferred to the internal degrees of freedom in the time available and consequently there is little loss. When the period of the sound wave is of the same order as the time taken to establish equilibrium, the sound wave loses a considerable amount of energy to the internal degrees of freedom which it does not regain. The absorption coefficient is therefore small at high and low frequencies and a maximum at the frequency corresponding to the reciprocal of the time taken to establish equilibrium. An expression for the absorption coefficient per wavelength is developed in Chapter 2 after Kneser (S)

where

Cv (r + Cv)

is the universal

IT Q i K, W

13 constant, is the heat capacity at constant volume per mole,is the vibrational internal heat capacity per mole,is 2 TT X frequency of maximum absorption,is 2 TT X frequency of the sound wave.

When JU the absorption coefficient per wavelengthis plotted against the frequency f » ^ bell-shaped curveis obtained which has a maximum where -T = — .

J X i r rSmall amounts of certain impurities can have a

K.w

12

very profound effect upon the relaxation times of gases. Collisions with these impurity molecules can inducetransitions in a vibrating molecule more easily than can collisions with molecules of the same type. Consequently the redistribution of energy between the internal and external degrees of freedom occurs more rapidly and the frequency of maximum absorption of the sound wave is thereby raised.

The frequency of maximum absorption increases linearly with the concentration of most impurities but In the single case of water vapour it is a quadratic function of the concentration (12).

E&fly measurements of the effect were made by Knudsen (7) and Chrisler and Miller (8 ) who studied the effect of varying humidity upon the absorption of sound in air in reverberation rooms. These measurements shewed that the absorption coefficient for air decreased slightly with increasing humidity. Knudsen (9) using commercial gases and wet and dry bulb thermometers to measure the humidity in a reverberation chamber, revealed a selective absorption region for air and oxygen between 3 ,000 and 10,000 cycle, secf^ depending upon the humidity. Kneser*s results (6) at 3,000 and 6,000 cycle, secf^ using oxygen indicated a quadratic dependence of the frequency of maximum absorption f^g^ upon the water molecule concentration h defined as

13

number of water molecules h = -------------------------

number of oxygen molecules

In particular

^max “ 1.67 % 10® h® cycle, sec.*^

This function is plotted in figure 1, page 14.Kneser and Knudsen (11) obtained

f = 1.75 X 10® h + 7.96 x 10* cycle, sec."^max

at 3,000 - 6,000 cycle. sec.~lKnudsen and Obert (12) using 98/ pure commercial oxygen in a reverberation chamber at 7,500 - 34,000 cycle, sec.” f ound

^max ^ 4.9 X 10® h + 6.1 x lo" h^ cycle. sec.“^

Knotzel (13) used a resonance tube method with a loudspeaker and condenser microphone working over the range 600 - 5,000 cycle, s e c . w i t h moist air. More recent measurements (14) using 99.6/ pure commercial oxygen gave

^max = 40 + 1.95 x 10® h + 1.32 x 10® h® cycle, sec."^

Thus there has been no systematic investigation into the phenomenon at frequencies below 600 cycle, sec.*^At lav frequencies the necessary control of temperature, humidity and gas purity present formidable problems.

The method used in the present work was first

14

13,000

b.ooo

lO

flG -O R t I . FR£9üENCy OF M AXIM UM fi ftS ORPTtOM

AeA INST Vi For oxy&e.M

15described by Reay (15) and subsequently used by Harlav ( 15 ) ( 17) to make measurements of velocity and attenuation in non­relaxing gases at low frequencies. The aims of the present work have been:(i) To redesign and improve the apparatus used by Reay and Harlow.(ii) To study the effect upon the absorption coefficient at frequencies between 90 and 1,200 cycle. sec.“ of the addition of small quantities of water vapour to oxygen.

Oxygen was chosen for the investigation rather than air because the relaxation absorption is larger, the nitrogen in air not shaving a relaxation effect in the frequency range considered.

The method involves the analysis of the imoedance variation of a cylindrical gas column near its natural modes in order to determine the absorption coefficient.

— — — ooO 00—“—

IS

CHAPTER 2 .

THE THEORY OF THE RELAXATION EFFECT.

In a polyatomic gas the number of vibrating molecules depends upon the temperature. The passage of a sound wave through the gas causes changes of temperature which are followed by changes in the number of excited (vibrating) molecules. These latter changes are not immediate and there is a characteristic time lag between the temperature change and the molecular transition process. The equation governing the transition between n^ moles of excited molecules and ng moles of normal

molecules is:

= K,n, - Oot:

where is the number of transitions from the excited state to the normal state per mole per second and Kg is the number of transitions from the normal state to the excited state per mole per second.For oxygen at normal temperatures n^ rig and Kg << K^.

For equilibrium between the number of excited > and ] normal ; molecules

- Foi = n at ^

17

Jk. ^ = K ©K, " a *

where n^Q is the number of vibrating moles at equilibrium and ngo Is the number of nonvibrating moles at equilibrium. K is the equilibrium constant and is given by Boltzmann’s Law as

K . F ®where F is a constant,

E is the vibrational energy per mole,R is the gas constant per mole,T is the absolute temperature.

Also n, 4- = N

where N is the total number of moles present which remains c onstant•Hence from

The solution of this equation is

_ - + e where A is a constant- K,t= A + €, since Kg

Thus readjustment after any disturbance takes place with a time constant /

18Let w be the angular frequency of the time

variation,From equations and

^juiOi zz Kj K (12^

Consider a small change with corresponding changes of K and ^ Ki .

j w - K ^ / k )+

For small deviations from equilibrium we may neglect the second term in brackets on the right.

Also An = — An^.

Thus

From equation

Thus from equations and

( ^ ) o , K A T = (' + K + ) A nt 0

The energy of the system must be conserved.thus

£ An^ 4 A t 4" p A v - ^ - Q @

19where Cy is the heat capacity at constant volume per mole, and V is the volume per mole.Now

A v') = 7. A T ®

Aw- Cv + ^

©and ^ c = — CA S

where c is the velocity of sound in the gas and ^ is the molar density given by

3 = - ^ ©where M is the molecular weight of the gas.Now

A(-pvr)=5 pAxr +

A -p = |^A(pw) - T ©

From equation

^ 3 = " (-4 ^) ^ = - 'S ( 4 ^ ) ©

From equations and (J )

Eliminating An, from equations 0 and 0 w e obtain

A T P 0

which from the quantum theory of specific heats is knavn

20

as the vibrational internal heat capacity. From equations and (3 )

Combining equations and (^we obtain

©

Cvt c : © l + K-l-

The complex value of c shows that there is aphase lag between the variation of the pressure and thecondensation. In order to determine the attenuationcoefficient from the complex value of c^ we write

jyc> =

where f is the frequency and A the wavelength.

The amplitude H of the vibration may be written

H He e-

Ho e.

byThe amplitude absorption coefficient cK is given

H = H,

where H and Hq are peak values.

21Thus by comparison of ?)and

f AS I r* —-

\ Z.

The absorption coefficient per wavelength is given by

y U = CXC X = ^ ©

Now since K « 1 we may obtain from equation

25

(CyCv + Cl + * v/K,

Rationalising the denominator

(cv + R- Ci.)(Cv+Ci.) Cv(ktCv) +23

Tan is given by the quotient of the imaginary and real parts of c^, which because <T< becomes

Thus tan y- 1 and we may write

toLO V = 2. SkA

Thus from equation

A — TT taA y

TTCv(^R+Cv)

C u K> wKi*4

22When yLL Is plotted against-cJ a bell-shaped

curve is obtained (figure 2 , page 23) which has a maximum where •The maximum absorption is given by

^ [-4)1 ®———ooO 00———

23

LU

Lu

<-oenou

LUCC UiLU

La.

y?d Moiia'W0S%y NO?iW\ yig y

24

CHAPTER 3.

THE THEORY OF THE METHOD.

The theory given below follows the general lines of the treatment by Reay (15), some modifications and additions having been made.

The gas is contained in a closed rigid cylindricaltube and longitudinal vibrations are excited by a planediaphragm at x = 0, vibrating in a direction parallel tothe axis of the tube. The longitudinal particle velocity %H at a point x is given by

where oA is the amplitude attenuation coefficientper unit length, is the propagation constant,

X is the wavelength,W is

is the frequency,A and B are constants to be defined by the boundary

conditions.Assuming the periodic force driving the piston is

Y = Y o

25

v;hich in the absence of all other forces imparts a particle velocity to the piston

jiob=

Zowhere Zo is the impedance of the piston.

The equation of motion of the piston under the influence of the driving force and excess pressure is

Z o = V - ®

where ol is the area of cross section of the tube, and is the excess pressure at x = 0.

The excess pressure at any point x may be written

e. e_ @

where ^ is the density of the gas,and Cj is the velocity of sound in the gas enclosed by

the tube.Also

where 2 -tis the impedance at x =-0,,^ is the particle velocity at x=-£ ,

is the excess pressure at x = £, .Equations to lead to the result

2 o ( A + B ) = t o -

26

Hence Ho -Y o e

o o

where the driving point impedance is given by

Z ^ O = Z . +

. /zi::iS£T\L T \25.-t-as< T;

The present apparatus was designed so that Zgiving

Zoo = Z o + o-S<^T t o t K

We shall now examine the variation of the driving point impedance in the neighbourhood of a natural mode of the gsifs column, assuming to be constant over a small frequency range. Zoo may be expressed in arbitrary units and the analysis is simplified if is taken as the unitof impedance.

Z o o = Z o + Cotk ( U+jv)

where \j => «K CV =

Let + = -CotK(u+jV)

_ T + ,x-t R + j X + /

0

27

Multiplying © by the complex conjugate_ 4v ^ (-R + j X - Q ( ’R-jX-i)

^ “ (K+jX+/)f R-AX1-I)Hence X* + > = % ^

The locus of the point (R, X) is shown on the Argand Diagram figure 3, page 28. It is the circle

- CotK2u)^-f — costth*^ 2u

which has centre (Cotk2*G > 0 ) and radius c o G. OP represents the modulus of C ot. K(o<-1-5 ,

H o w Zoi = Z o ' + R + j X

The impedance Z© is represented by the vector P^O and theresultant Z©o is represented by P^P.

FromP ^ S t n K Zc< C________

cosh 2<x£ — cos 2. 12

X = @C OS K lo((. — cosZ^-2-

The points A and B are given by X - 0,when X = 0 5jn 0

A is p — SI o K 2o< £.______ Y _ ^cosh loci + I A U

B is -K = ------- X = OcosK 2oc£ - I

28

tL0

ïlctAUJa.rH

H(Tr-in

M

H

U

O

fv&ORÊ. H- Tt\PEl>R»4Ce. fl&RiKST F(tE( 0(LHCY

^ R e A<-“T*\« c e o f vt^

Now at B

29= + *

2 ^e = ^Mir

= % NTT< T

where N Is an integer.Each integral value of N corresponds to a natural

mode of the gas column of which the length is an integral number of half wavelengths. OA is the impedance at the anti-resonant frequency at which the length of the tube is an odd number of quarter wavelengths.

Two assumptions are made concerning oC and the validity of these will nav be examined.(i) The value of c< is constant over the small frequency range on either side of the natural mode.(ii) The value of is small so that O A ^ O .

In practice increases with frequency and the locus of P is a lew pitched spiral. However P moves over the greater part of the circle while the frequency varies over only a few cycles per second near the resonant frequency and calculation shovs that the effective diameter of the circle changes by less than a few tenths of 1% over the range considered.

AlsoOA = Okt

cosW 2 + I

Ac ~ cosecW

30

O (K __ t:cunk oc tAB 2 coscck 2 o( &

Thus a second circle diagram may be plotted with the value of OA calculated from the above equation using oC from the first circle diagram. The value of oCobtained using the second circle diagram does not differ significantly from the first value and consequently In most cases only one circle diagram is necessary.

OP2 in figure 3, page 28, is considered to be constant over the small frequency range. This is permissible except where varies rapidly with frequency. Referring further to figure 3, the point P moves anticlockwise around the circle as the frequency is increased. The magnitude of the vector PP^ representing the impedance of the system is plotted against frequency in figure 4, page 28.

In the present method values of the impedance Z ’oo are determined in the neighbourhood of a natural mode and a curve similar to figure 4 is plotted. The circle diagram figure 5, page 31, may then be constructed as follavs;(1) The diameter of the circle PgPg is given by the impedance difference IM, figure 4.(ii) P^C figure 5 is given by ON figure 4 where N is the mid point of IM.(iii) OP2 is estimated and corrected by successive approximation as described belcw.

The frequency may then be determined for a number

31

R

FlGOftE. 5. Tne. ?«.AC.TiCfti. c»«cu£ DimGRAM VRgftCXt tKCfc. OF Zo -FVty

32

of phase angles on either side of OR by reference to the impedance against frequency curve.

From and

. s..% oL^

For a small frequency range on either side of ^ = 0 , the graph of tao <j> against f is a straight line figure 6, page 31. The slope of this line at tan - 0 is

4ir 2,

oC = iJLC-p. s

The frequency at which bai\^ = o is given by fjg

ifxrffi 2 - % nIttCTC h .N

Hence _ tt N■ T T j T

Thus the attenuation coefficient may be calculated from the slope and intercept of the tan. against f curve, providing the length of the resonance tube is known.

In previous work using tubes of smaller radius the

33/

value of Zo was estimated assuming a linear variation with frequency between the anti-resonant frequencies. It was not possible to use this method in the present work because of the low natural frequency of the diaphragm and the lack of

tsmooth variation of Zo with frequency. Consequently aI

value for Z'o was estimated from an examination of the/impedance curve. As a first approximation "Zo was assumed to

be equal to the mean of the impedance values at the peak andtrough of the Zoo against f curve and a corresponding circlediagram and against f graph were constructed. Theabove theory shovs that the ban against f graph should bea straight line and the effect of an incorrect estimate forZo is shown in figure 7, page 34. The true value of "Z o.4qyielded the unbroken straight line. If the estimated valueof Zo^was high or lew the against f graph was displacedand slightly curved. The slope of the tangent to this curveat bo-n^= 0 yielded an approximate value for the attenuationcoefficient. The direction of curvature of the graphenabled the sign of the error in Zo to be determined. Asecond estimate for Zo^was then made, the circle diagram wasredrawn and a new ban against f graph constructed. . This

/second estimate for Zo was usually sufficiently accurate to enable a straight line to be drawn through the points on the to-r> (j> against f graph.

The above analysis has been described for a positive reactance of ZL ( Z^,increasing with frequency), some modes a negative reactance of Z © was encountered ( Z<

34

U-

u.

35decreasing with frequency). The corresponding impedance plot and circle diagram are shoivn in figures 8 and 9 , page 36 The attenuation coefficient is derived in an exactly similar way to that described above.

———ooO 00—""Measurement of the Impedance of the System,

If the amplitude of vibration of a point on the diaphragm is Ho , the velocity is given by

Ho = U) He=Z 2.TC Ho

Further if the force acting upon the diaphragm is

Then1ho| = \Vol

I /

where Z'oo is the driving point impedance

Consequently ( ZLo| = ;

In the present apparatus the driving force was directly proportional to the current Iq through the moving coil

•••

Also the current through the moving coll was maintained at such a value that the amplitude of vibration Ho was constant

Hence / j\ Zoo 1 ""2

o

36

c 5

% C/1AaiCLZ

M

N

LO

F i g u r e 8. % Mp£>flNCE FRS( üEK)c\j . (^REACTAMCa. OF 7 o — V£ ^

V

p>F i g u r e <\, T H S P r a c t i c a u c ^ rcu e D v r g r r m

( RsfCTAMcE OF Zo — VE^

37Only relative values of the driving point impedance are required for application of the method used in this work. Consequently if the current required to maintain the constant amplitude is measured and divided by the corresponding frequency, an impedance curve may be plotted and the absorption coefficient determined as described earlier in this chapter.

The amplitude of vibration was maintained at a constant value by an optical method described by Smith (18).A system of Newton’s Rings was set up between a thin plane glass disc cemented to the centre of the diaphragm and a small lens held very close to the disc. As the amplitude of

vibration of the diaphragm was increased the Newton’s Rings passed through states of zero visibility, when the whole field of view was uniformly illuminated, at certain critical amplitudes which depended upon the wavelength of the light A.The critical amplitudes were as follows; 0.1914A, 0 .4393X,

0.5886X, 0 .9383X, 1.1883X, 1.4380X, I.688OX, 1.9379X, 2 .1 8 7 9 X . . .

In practice the uniform appearance of uhe field at the critical current setting provided a very sensitive method for reproducing the constant amplitude of vibration required by the theory.

When the diaphragm was vibrating non-uniformly,Instead of a uniform illumination over the whole field at the critical current, the uniformity was obtained in a band across the field of view. As the current through the moving coil was increased slowly the band moved perpendicularly to itself

38across the field. This phenomenon proved very useful in confirming that the vibration of the diaphragm was satisfactory.

The first critical disappearance of the rings with mercury green light 546lA^ was used for all the observations described. This gave a constant amplitude of vibration of 1.045 x 10“^cm.

———ooO00*—"

39

CHAPTER 4.

THE RESONANCE TUBE. REFLECTOR AND LOUDSPEAKER.

The resonance tube was fitted with a reflector at one end and a loudspeaker at the other. The following features were considered desirable when designing the system(i) Provision for continuous flushing of gas through the resonance tube.(ii) Provision for evacuating the tube without disturbing the optical system or causing a pressure differential to appear across the loudspeaker diaphragm.

(a) The Resonance Tube.The resonance tube was a seamless duralumin tube

nominally 4j inches internal diameter with a J inch wall and was approximately 170 cm. long. The inner surface of the tube was polished with a rotary polisher and appeared to be smooth and free from flaws.

The internal diameter of the resonance tube was measured at both ends and the results are shown in table 1, page 40. The mean internal diameter of the tube was 11.42 ± 0.01 cm. The internal diameter of the tube set an upper limit to the frequency that could be used. According to Lamb (3), providing X > 1.7 x diameter, transverse

40

(PoCQ

OHg

CO§OHeEhëMêg

# •E Bo o

lO oiH tor4 rHr4 rH

O lOrH rHr-i rHr4 rH

O Or4 tofH rHr—1 rH

lO lOrH 03Tt« kHrH rHrH rH

Pg MH KMK WO <EH MO Pg PkH qK P

BO

-HSi

i<MnR<

HgMOïz;SoenWtewK54kO

SSsppgEh%M

gm<EH

41vibrations cannot be propagated, the wavefront is plane and the Helmholtz-Kirchhoff theory is applicable. In the present case the upper limit to the frequency was about 1,700 I cycle, sec."^

The length of the resonance tube from the reflector face to the other end of tne tube was measured using a Fitter Stick Micrometer Gauge and a straight edge across the open end of the tube. The gauge consisted of a set of rods of standard lengths with plane ends which could be screwed together on to a vernier micrometer to measure lengths up to about 300 cm. to an accuracy of about 0.001 cm.

Preliminary measurements carried out using different combinations of rods established the reproducibility of the readings. In order to check that the reflector and diaphragm were accurately parallel, the length of the resonance tube was measured in four positions near the inside wall separated by 90®. The results are shown in table 2, page 42. The measurements were carried out at room temperature on four occasions throughout the day. The Fitter Gauge reading yielded the separation between the reflector and the end of the tube near the diaphragm. In order to obtain the true diaphragm-refleetor separation the following corrections had to be made:(i) A negative correction for the gauge zero error.(ii) A negative temperature correction due to the contraction of the gauge at temperatures below 15®C.(iii) The correction of all the readings to a standard

Temp.oc / Orientation 0^ 90° 180° 270°13.6 167.7278 157.7332 157.7388 157.735414.1 157.7313 157.7355 157.7396 157.735214.6 157.72 99 167.7368 157.7419 157.735114.9 157.7315 157.7372 157.7422 167.7382

Correct for gauge zero error13.6 157.7258 167.7312 157.7368 167.733414.1 167.7293 157.7335 157.7375 167.733214.6 167.7279 157.7348 167.7399 157.734114.9 157.7295 167.7352 157.7402 157.7352

Correct for contraction of gauge:13.6 157.7247 157.7301 157.7357 157.732314.1 157.7283 157.7325 167.7366 167.732214.6 167.7270 157.7339 157.7390 157.733214.9 157.7285 157.7343 167.7393 157.7353

oCorrect to 13.6 C157.7247 157.7301 157.7357 157.7323157.7254 157.7306 157.7347 157.7303157.7232 167.7301 157.7352 157.7294157.7237 167.7294 167.7344 157.7304

Mean 167.7245 157.7300 167.7350 167.7306- overlap 157.7181 167.7300 157.7325 167.7230+ gap (small dm.) 167.7537 157.7530 167.7705 16 7.7560

+ gap (large dm.) 167.8018 167.8154 157.8137 157.8057

42

Mean small dm./ref lector separation = 167.761 0.010 cm .@13.6®CMean large dm./ref lector separation = 167.810 d= 0.008 cm .@13.6®C Change in length/®C. = 0.00379 cm .

TABLE 2. LENGTH OF THE RESONANCE TUBE, (cm.)

43temperature of 13.6®C.(iv) A negative correction due to the tube overlapping its flange at the loudspeaker end.(v) A positive correction due to the gap between the diaphragm and the flange. This correction was different for the small and large diaphragms used in this work.

(iv) and (v) were determined using a straight edge and depth gauges.

(b) The Reflector.One end of the resonance tube A figure 10, page 44,

was threaded to take the bronze flange T of the reflector.U was a massive mild steel plate ij inches thick bolted to the flange T at right angles to the axis of the resonance tubeThe brass piece V carried a mild steel plunger W whichfitted through the plate U in a hole of diameter ^ inch. Theend of W was lapped smooth with U when the assembly wasbolted up and W was fully advanced. When W was withdrawn, the gas could leave the resonance tube at Z and pass out through X. W was fitted with a gas tight rubber 0 ring seal at Y.

(c) The Loudspeaker.At the end remote from the reflector the resonance

tube was threaded to take the bronze flange B of the loudspeaker, figure 11, page 45. The main assembly of the loudspeaker consisted of the large cylindrical magnet E

clamped between the mild steel plates D and F by six mild

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steel bolts. The two undercut trapezium grooves P were fitted with rubber 0 rings to ensure a gastight seal. The diaphragm (not shown in figure 11) was mounted between the mild steel plate J and the bronze section C. The gas passed into the loudspeaker through tube M, then through the inside of the magnet E, tubes 0 and N and into the resonance tube at L when the plunger K was withdrawn. K was fitted with a piston 0 ring seal screwed into plate C and could be screwed out by means of a chain and sprocket from outside the apparatus. Thus a continuous flav of gas could be obtained through the loudspeaker, around the diaphragm and into the resonance tube.

The mild steel cylinder R was screwed into F so that the annular gap between R and D for the moving coil was 0.05 inch wide. The uniformity of the magnetic flux in this gap was checked using a specially constructed search coil and a ballistic galvanometer. The flux density around the gap was found to be uniform to better than =t. 1%.

Holes S were drilled to enable the brass tube 0, which carried part of the optical system, to be inserted and extracted from R. H was a brass insert with a piston 0 ring seal and a flat glass plate cemented with Araldite

epoxy resin over the end at an angle of 85^ to the axis in order to avoid undesirable reflection of light into the optical system.

Considerable care was taken in the design and

47mounting of the diaphragm. Preliminary measurements were made using a simple circular disc cut from duralumin in a lathe and mounted in rubber 0 rings as described by Harlav (16). However, it was found difficult to obtain uniform vibration of the diaphragm under these conditions because the actual clamped area was not clearly defined and was liable to change if the diaphragm was removed and remounted. It was considered vital to define the clamped area with great precision. Consequently, the type of mounting adopted was a firm metal to metal clamping using circular duralumin annular gaskets on both sides of the diaphragm between plates J and C in figure 11. A thicker duralumin disc of slightly larger diameter than the bore of the resonance tube was cemented to the thinner diaphragm so that the flexing of the latter took place outside the bounds of the resonance tube. This system proved very satisfactory at the lower frequencies but the Impedance was too high above about 500 cycle, sec.-l It was not possible to reduce the Impedance by reducing the thickness of the diaphragm because duralumin of uniform thickness and good quality was not obtainable thinner than 0.300 ram. It was necessary to devise some other means of reducing the impedance and this was done by increasing the diameter of the diaphragm and using circular precision duralumin annular gaskets to clamp It at the periphery of the trapezium groove in plate D figure 11.

The type of diaphragm used at the higher frequencies is shavn in figure 12, page 48. A was a disc cut from HS10l?P

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(B.S. 1470) aluminium alloy sheet 0.308 mm# thick. It was turned in a lathe to a diameter of 21.2 cm., heated for 12 hours at about 350^0. between two flat steel plates and allowed to cool slowly to room temperature. B was of a similar material but 0.910 mm. thick and 11.0 cm. diameter and was also turned circular and heat treated as above. B WQs carefully cemented concentrically to A using an epoxy resin adhesive Araldite AY 105. The four holes F were drilled 2 mm. diameter to alio?/ gas to flew from one side of the diaphragm to the other when mounted. The coil former D was of stiff paper 1 inch long wound on an iron pipe turned down to 1.52 inches diameter. The coil C consisted of 350 turns of 45 S.W.G. enamel covered copper wire and was wound on the paper former in a lathe. The coil was impregnated with a hot setting epoxy resin Araldite AY 105 which when hard proved to be extremely rigid and not liable to creep. The former was cemented concentrically to the diaphragm with a cold setting epoxy resin adhesive Araldite AV 123B. E was a thin glass disc forming part of the optical system. The leads to the ends of the coil were brought out, twisted together, coiled in a loose spiral, fed through holes 0 and M, figure 11, and out through a gastight seal.

The diaphragm was mounted centrally in the loudspeaker by fitting it over four lengths of cotton thread over the tube R. When the loudspeaker was bolted up the threads were withdrawn leaving the diaphragm coil free to vibrate in the air gap of the magnetic circuit. In order to

50check that the diaphragm was vibrating satisfactorily the currents to produce successive disappearances of the fringes were plotted against the corresponding amplitudes of vibration. The resulting graph is shown in figure 14, page 51. The experimental points all lie on a straight line passing through the origin shaving that the diaphragm was vibrating satisfactorily.

The resonance tube, reflector and loudspeaker were designed to be gastight by the provision of rubber 0 ring grooves, ^here 0 ring seals were not provided, the joints were sealed with apiezon vacuum grease type N and Q wax. The gastightness of the system was checked by connecting it to a manometer, evacuating and observing the pressure rise overnight. Leaks were found due to the porosity of some of the loudspeaker castings and also the magnet. These were overcome by flooding the surfaces of the castings with solder and coating the outer surface of the magnet with Araldite type AV 123B. All exposed surfaces were then given two coats of glyptal lacquer and left to dry for ten days, after which time any leaks present were found to be negligible.

Before the initial filling with gas and subsequently on changing the type of gas used, the tube was evacuated and flushed many times over a period of several days in order to minimize the effect of adsorbed impurity gases on the walls of the tube.

51

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52(d) The Optlcel System.

The amplitude of vibration of the diaphragm &as maintained constant by the optical method described on page 37. One side of the 1 cm. diameter glass disc E (figure 12, page 48) was roughened with carborundum paste, cleaned, coated with optical black and cemented to the centre of the diaphragm.This ensured that the fringes were formed only between the lens and the near face of the glass disc, unwanted reflections from the other face being eliminated. A lens T was mounted on tube G at Q as shown on page 48, figure 13, which is approximately three times the scale of figure 12 . The plano­convex lens T had a radius of curvature of about 200 cm. and the plane face was cut at an angle of 85° to the axis. W was a brass bush carrying the lens T and connected to G by three screws V passing through springs U. Adjustment of the screws V using a long screwdriver enabled the Newton’s Rings to be centralized.

The Newton’s Rings were viewed through the system shown in figure 15, page 53. The point source of light was a Siemens Ml mercury discharge tube operated from a 24 volt D.C. supply to avoid stroboscopic effects. The arc current was about 0.5 amps, and a series resistance of about 24 ohms was included to limit the current. The mercury light was focussed on to a stop by means of a double condenser lens.This condenser lens consisted of two plano-convex lenses cemented together with an Ilford colour filter type 807 (mercury green) between them. This filter transmitted the

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54mercury green line at 5461 A® giving much clearer interference fringes and improved sensitivity to the amplitude detection. The light from the stop was reflected by the adjustable glass plate which was set up at approximately 45® to the'axis of the tube. The stop was arranged to be at the focus of the bloomed objective (3 inches focal length and 8 inches working distance) and thus the fringes were formed by parallel light.

The fringes were viewed through the Ramsden eyepiece (magnification X 15) mounted in a telescopic tube sliding in the larger tube, which together with the side tube contained the other optical components. The interior walls of the tubes were blackened to minimize stray reflections and careful adjustment of the components enabled high quality Newton’s Rings to be obtained.

———ooOoo**"***

55

CHAPTER 5.

TEMPERATURE CONTROL AND MEASUREMENT.

(a) Temperature Control.The resonance tube, loudspeaker and reflector were

supported by three suitably curved wooden supports mounted on ball races so that the system could be moved easily into and out of the interior of a double walled tank. The tops of the wooden supports were cushioned with foam rubber to minimize the vibration imparted to the system. The tank was 9 ft. long and constructed of 12 S.W.C. galvanized iron as shown in figure IS, page 56. The inner tank was 11 inches wide X 12 inches high and the outer tank 18 inches x 18 inches# Water covered the inner tank to a depth of 3 inches and was circulated between the inner and outer tank by means of eight Archimedian screw stirrers. These had ports cut at top and bottom such that the water was circulated rapidly across the tank from end to end as shown in figure 17, page 57. The stirrers were mounted in copper tubes 2f Inches internal diameter and consisted of 3 inches pitch spirals of 18 S.W.G. copper strip soldered to ^ inch diameter brass rods. The brass rods were fitted with nylon bearings where they passed through the brass end plates in the tubes. The bearings were machined from Polypenco Nylon 610 rod, required no

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58

lubrication and were renewed only once during the course of the work described. The stirrers were fitted with triple groove pulleys and were driven by a series of welded plastic belts from an English Electric single phase i H.P. alternating current motor mounted on anti-vibration mountings at one end of the tank. Welded plastic belting was used to minimize vibration and proved to be relatively trouble free and easily maintained. The drive from the motor to the first stirrer was by an endless rayon vee belt because this was subject to the greatest stress. A time switch was fitted to the electric motor so that it could be switched on automatically early,in the morning in order to reduce wear of the plastic belts and stirrer bearings which would otherwise have been operating all night.

The water was heated by eight 450 watt domestic smoothing iron elements enclosed in copper sheaths filled with transformer oil. Each element was placed near the exit port of a stirrer and the electrical connections were as shown in figure 18, page 57*

In order to reduce heat losses from the system the base and sides of the outer tank were covered with a layer of felt 1 inch thick. The ends of the inner tank were closed with tightly fitting wooden blocks 1 inch thick with suitable apertures provided for the telescope, gas inlet and outlet pipes, electrical connections and valve control rods. Cotton wool was packed into any remaining crevices. The air inside the inner tank-was circulated by

59

a fan driven from outside the tank via a flexible shaft by a small electric motor. An aluminium baffle 11 inches wide was placed astride the resonance tube from the loudspeaker to the reflector to assist the circulation of air throughout the whole of the interior of the tank.

In the past in similar work (16) temperature control has been achieved by the use of a long glass regulator bulb filled with toluene which expands and contracts with temperature rise and fall and actuates a mercury control switch. Preliminary measurements were carried out to test the feasibility of thermistor temperature control in the apparatus and it was decided that such control would be more desirable. A thermistor control system does not obstruct the water circulation, is not prone to breakage, is easy to construct and flexible in use.

The heaters were switched on and off by the control circuit shown in figure 20, page 60(19). Essentially this is a 50 cycle, sec."^ A.C. bridge circuit incorporating a thermistor, follaved by an amplifier and a phase sensitive detector. A relay in the anode circuit of the last stage operates a slave relay carrying the current to the heating circuit. The temperature of operation could be selected by coarse and fine switches on a control unit with reference to a previously determined calibration graph for the thermistor concerned. The work described here was performed with the apparatus at about 30^0., however provision was made for operating at higher and lower temperatures by

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61altering the bridge ratio* In addition to this the heating elements were run considerably below their nominal rating so that the system could be readily adapted to operate at higher temperatures by Increasing the input to the heaters.

It was desirable to minimize the thermal lag in the system and care was taken in designing the mounting system to ensure that the thermistor was in good thermal contact with the circulating water. The mounting is shavn in figure 19, page 57. The thermistor bead B was soldered to the very thin copper disc C fixed at one end of a watertight box attached to the copper tube D through which passed the coaxial cable A carrying the output from the thermistor. The thermistor was a type M52 supplied by Standard Telephones Ltd. and had a temperature coefficient of resistance of about 4^®C. at 20®C. and a resistance of about 500 ohms. Thermounting was placed on the top of the inner tank in a region of maximum water circulation.

Overall control was such that the temperature of the tube could be maintained over all its length and a period of several hours within the accuracy of the measurement by the thermometers i.e.zL 0.02®C. at 30®C. The control system proved in practice to be very efficient and operated continuously for periods of several months without defect or attention.

62(b ) Temperature Measurement#

The temperature of the tube was measured with four mercury in glass thermometers supplied by Griffin and George Ltd# These thermometers had a range from -5 to-b50®C# divided at O.l^C. intervals and were calibrated for 17#5 cm. vertical immersion by K.P.L# to an accuracy of ± 0.02®C.The thermometer bulbs were immersed in glycerine contained in four metal cups cemented to the resonance tube with epoxy resin at equal intervals along its length. The thermometers passed through corks inserted in chimneys from the inner tank to above the surface of the water.

The temperature could be estimated to O.Ol^C. using a magnifier and after a period of about four hours from starting up the stirrers, the temperature was constant to within db 0.02®C. along the tank for several hours.

—“ • ooO OO”*»*

63

CHAPTER 6 .

FREQUENCY MEASURE!.'!EN':

The comparison of frequencies of the order used in the present work with high precision over a small interval of time requires a device that is capable of indicating fractions of a cycle. The method used to determine the frequency in the present work was comparison with a stable quartz crystal oscillator using two synchronous

I

motors and a photographic technique.The quartz crystal oscillator was a Frequency

Standard Type 761 manufactured by Airmec Ltd. The crystal frequency was 1 Mcycle. sec.*^ and outputs of 100 Kcycle. sec.“ 10 Kcycle. sec."l, 1 Kcycle. sec.'l, 100 cycle, sec."^ and 50 cycle. sec.“l were derived by dividing circuits. The frequency stability of this instrument could be checked in two ways :(I) By beating the second harmonic of the 100 Kcycle. sec,"l output with the 200 Kcycle. sec.-l B.B.C. carrier wave transmitted from Droitwich. This latter frequency is maintained to better than 5 parts in 10®.(II) By using the 50 cycle. sec.“ output to drive a clock and checking the timekeeping with the B.B.C. time signals.This gives also the sign of the departure from 100 Kcycle. sec7

64

The frequency stability over a period of several days is plotted in figure 21, page 65. Long term observations gave the standard frequency as 100,000.7 ± 0.3 cycle, sec.-l over periods of several months.

The oscillator used to supply the loudspeaker was an RC Generator Z 9.060.69 manufactured by Philips and fitted with a slŒV motion frequency dial. The frequency range covered by this instrument was 3-10,000 cycle, sec.'^ and the frequency stability was quoted as being better than 0.1^/hour, one hour after switching on. In fact when supplied from a constant voltage transformer (Advance CVH 125A) the stability was about ten times better than the above figure especially after three hours (figure 22, page 66). The distortion was stated to be less than 0.5^ and was not checked but the waveform was displayed upon an oscilloscope during the experiment and at no time was any distortion apparent.

The 1 Kcycle. sec.~l output from the standard oscillator and the output from the RC oscillator were amplified by two and one stage amplifiers respectively (figures 23 and 24, pages 67 and 68) and applied to the A.C. windings of two Phonic Motors A811-C supplied by Muirhead and Co. Ltd.The phonic motor rotates at a rate proportional to the input frequency f such that the number of revolutions per second is f/n where n is the number of rotor teeth. The motors used had six pole stators ànd the rotors were iron rings with 100 teeth giving a usable frequency range of

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The phonie motors P (figure 25, page 70) were mounted on opposite sides of a large light-tight wooden box and each motor drove a revolution counter G (Counting Instruments Ltd.) via a flexible coupling F. Each revolution counter was fitted with a brass wheel B with a circumference marked into 100 equal divisions. Two fixed cross wires X were mounted immediately before the front faces of the brass wheels. The counters and brass wheels could be photographed in a single frame by means of the camera constructed at the opposite end of the box. The lens L was a Wray 2 inches f 4.5 Supar set at f 32 giving a frame size of 25 x 25 mm. on 35 mm. film. The counters and front faces of the brass wheels were not coplanar so that the depth of focus had to be chosen such that a clear image of both was obtained. A shutter was not used and the illumination was by Mullard LSD 3 tube and associated circuit as shown in figure 25, page 70, This gave a flash duration of approximately 150y/sec. so that blurring of the image was not apparent even at the fastest revolution speed of the counters i.e. 15 r.p.s. The camera D was designed to take 100 ft. spools of 35 mm. film to avoid frequent loading and unloading of cassettes.

Recording was on Kodak Tri-X panchromatic film developed for 10 minutes in Kodak D 75 developer and fixed in Kodak acid fixing salt with hardener. Very clear negatives were obtained which could be read without strain

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using a Kinderman table viewer,’ A positive print from one of the negatives is shown in figure 27, page 72.

In practice the counters were photographed at about one minute intervals and comparison of the number of revolutions made by the two motors (estimated to 0,001 revolution) gave the unknown frequency since the standard frequency was knavn very accurately. The unknown frequency could therefore be determined to about one part in 10^, At the lower frequencies the slower phonic motor could be synchronized with the second harmonic of the unknown frequency thereby increasing the accuracy,

———ooO 00*“ ••

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CHAPTER 7 .

BIPED ANGE MEASUmiHNT.

In order to calculate the impedance of,the system at a particular frequency it was necessary to divide the current through the moving coil at the first critical amplitude, by the frequency. The frequency was measured by the method described above and the current at the first critical amplitude by the circuit shown in figure 28, page 74 • The current through the moving coil was controlled by adjusting the Sullivan and Griffiths dual dial non-reactive resistance box (0-10,000 ohms) until the first disappearance of the fringes was obtained. The alternating current was measured by means of the vacuum thermojunction.and square law scale of the Cambridge Unipivot Galvanometer. The setting of the current was repeatable to better than 0.5^. Three thermojunctions were used with maximum current readings of 5, 10 and 20 milliaraps. The linearity of the galvanometer thermal scale reading with the input current to the thermojunctions was checked using a D.C. supply, standard resistance and vernier potentiometer. The relationship is shown in figure 29, page 75. The departure from linearity of the indicated current was always less

than 0.7^.

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A small dark room was built at the loudspeaker end of the tube so that the observer could view the interference fringes under conditions in which his eye would be most sensitive. The RC oscillator, decade resistance box, galvanometer, camera and motor control switches were arranged conveniently around the dark room so that the procedure was efficient and could be adequately performed by only one observer. The galvanometer could be read using a low power shaded light.

———ooO 00— — —

77

CHAPTER 8 .

HUÎÆIDITY MEASUREMENT.

The principal techniques in use for measuring humidity are based on wet and dry bulb, mechanical, dewpoint, electrical and gravimetric hygrometers.

The wet and dry bulb hygrometer consists essentially of two thermometers, one with a dry bulb and one with its bulb covered with a moist cloth. The thermometers are ventilated and the relative humidity can be calculated from the difference in readings of the two thermometers due to the evaporation from the wet surface (20). The method is much used in meteorology but was considered unsuitable for the present experiments because of the disturbing influence of the wet bulb thermometer.

Mechanical hygrometers are based on the change in length of hairs or fibres when subjected to a change in humidity. In commercial instruments the change of length operates an indicating or recording mechanism calibrated in relative humidity. These instruments suffer from hysteresis effects and lack of stability.

Dewpoint instruments consist of a device for Icv/ering the temperature and a means of measuring the temperature at which dew forms i.e. the temperature at

78which the gas is saturated with vapour. The relative humidity may then be obtained easily by reference to vapour pressure tables. This method has been widely used in practice but is not particularly suitable for low values of relative humidity.

Electrical hygrometers depend upon the variation in electrical resistance of a film or block of moisture absorbing material. The electrical resistance is usually measured with an A.C. bridge circuit. These instruments are used in meteorology and industry for continuous recording and control. They are however often unstable and require frequent recalibration for accurate work.

Gravimetric methods of hygrometry are fundamental and are used to calibrate most of the above instruments.The principle is to pass the moist gas slowly over a moisture absorbing chemical and determine the water vapour present by increase in weight of the chemical. Phosphorus pentoxide is normally employed for greatest accuracy in gravimetric work.

Having regard for the above considerations it was decided to use a gravimetric technique for measuring the relative humidity in the present work. The required value of humidity was produced by introducing a weighed quantity of distilled water into a side tube of the gas supply to the resonance tube (figure 30, page 79). The gas flow was diverted through the side tube and the water vaporized and was carried into the resonance tube. The

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gas flow was cut off and the system was left overnight in order that the gas could distribute itself uniformly.After the attenuation experiments had been carried out on this sample of gas, it was flushed out of the resonance tube with dry gas through two vertical drying towers with large exposed areas of Analar Grade phosphorus pentoxide. These drying towers were weighed before and after the passage of gas.

Agreement between the moisture inserted and recovered was within about 2 mgm. in weights up to 50 mgm. Each drying tower weighed approximately 130 gm. and could be weighed to an accuracy of i 0.1 mgm. The second drying tower was used to check that the first was performing efficiently. The drying towers were connected to the rest of the system with B 14 conical glass to metal joints. Gastightness was achieved by means of P.T.P.E. conical sleeves manufactured by the Loughborough Glass Co. Ltd. Weighing errors due to greased joints were thereby avoided and results made more reproducible.

The volume of gas in the resonance tube system was calculated from the known dimensions, A knowledge of the water content, volume and temperature enabled the humidity to be calculated.

m»"»OO0 OO""*

81

CHAPTER 9.

GAS PREPARATION AM) PURIFICATION.

(a) Air.The functioning of the apparatus was checked

with air since there has been more work done on this gas than other gases below 1,500 cycle, sec."^ Since the experiments were performed close to the Battersea Power Station it was considered desirable to use medical air for the preliminary experiments rather than atmospheric air of unknown and possibly varying composition. The medical air was supplied by the British Oxygen Company who provided the following analysis:

NitrogenOxygenArgonCarbon dioxideHydrogenNeonHeliumKryptonXenon

78.05% by volume 21.00% " "0.93% " M0.03% " “vol. in 33,000 vols. Air

” 55,000 “ "” 185,000 ” 20 X 10^* “Ü lYo « » »

83The air was freed from carbon dioxide and water

vapour by the purifying system shown in figure 31, page 83. The air entered the system at J and passed through the drying bottles B which contained caustic potash pellets K.The gas passed into the drying trap C which was surrounded with a mixture of solid carbon dioxide and acetone. Glass wool inside the trap improved its efficiency. Tubes D and E were packed with calcium chloride for further drying and F contained a carbon dioxide absorbent with indicator.Final drying was achieved by tube G with a large exposed area of Analar Grade phosphorus pentoxide and drying trap H similar to C.

The purifying system was constructed mainly from pyrex glass. For safety and convenience some connecting tubes were constructed from seamless flexible metal tubing with joints of ground cones made gastight with apiezon N grease. Rubber tubing was avoided on the grounds of being a possible source of contamination.

(b) Oxygen.Relaxation frequencies are very sensitive to

minute traces of impurities and it was therefore considered very important to have the oxygen analysed and also to check the results with oxygen prepared by an entirely different method.

The first source of oxygen used in these experiments was a cylinder supplied by the British Oxygen

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Oxygen 99.5% by volumeArgon 0.5% ** **Carbon dioxide 1 vol. in 200,000 vols. OxygenCarbonaceous compounds 1 100,000 ”Hydrogen 1 ” ** 20,000 ”Nitrogen A traceCarbon monoxide Nil

The second source of oxygen was a method described by Scott (21). A cylindrical furnace was constructed using a copper tube 6 cm. diameter and 70 cm. long wound with a nichrome heating wire insulated with asbestos. The tube was heat Insulated with micafll and mounted in a larger tube at a suitable height above the bench. The heating element was supplied from a variable voltage transformer manufactured by Philips and the temperature measured by a mercury in glass thermometer with a range of 0-300^0. This arrangement enabled the temperature of the furnace to be controlled accurately within a few degrees.

Approximately 1 Kgm. of Analar Grade potassium permanganate was placed in a pyrex glass tube of slightly smaller diameter and slightly longer length than the furnace tube. The glass tube terminated in a smaller diameter tube plugged with glass wool and fitted with a glass stopcock and B 14 ground glass cone. ’Vhen the large

85tube was inserted into the furnace the stopcock and cone were at such a distance that their efficiency was unimpaired by the heat. Figure 31, page 83, shows the furnace A connected to the remainder of the purifying system which was the same as that described in (a) above.

The furnace was raised to a temperature of 150^0., the glass tube was connected to a manometer and evacuated for at least 48 hours. The temperature was then raised slowly to about 200°C. when oxygen began to be evolved slowly. Pumping was continued for one hour in order to flush out the generating system. The oxygen was then passed through the purifying system into the resonance tube. When the reaction was 80% complete the generator was shut off from the purifying system and allowed to cool.

The potassium permanganate used to produce the oxygen was supplied by Hopkin and Williams Ltd. and was analysed as follows:

Maximum limits of impurities;Insoluble matter 0.1%Chloride 0.01%Sulphate 0.01%Nitrate 0.08%Arsenic 0.0002%

Hoge (22) quotes the impurities in oxygen prepared

867by this method as being not more than 2 parts in 10 .

"""OoO 00"""

87

CHAPTER 10.

' HESULTS AND DISCUSSION.

(a) Air.The results obtained using medical air in the

resonance tube are shown in table 3, page 88. The value ofcx^^^ obtained in column 4 has been corrected in column 5 for the small contribution due to relaxation in oxygen as determined in this work. The attenuation coefficient also varies inversely as the square root of the pressure

and the values of oC obtained are referred to 76 cm. Hg. pressure in column 6 . The error in the value of Xyg so obtained is about 3% and is due to the uncertainty in estimating the slope of the tan cj> against f graph.

The value ofcKyg obtained at 629 cycle, sec."^ was some 250% higher than theory would indicate. This was not entirely unexpected because the vibration of the diaphragm was non-uniform at about 600 cycle, sec.”^This was apparent from the non-uniform disappearance of the Newton's Rings as discussed in Chapter 3. The probable explanation of this phenomenon was that the diaphragm was vibrating about a chord. The requirement of the theory of the method is that the diaphragm should vibrate uniformly, consequently an increase in absorption is to

88

0H§1E-<S

HiCOwKCL

ië

O *—1iH«

1 Oo 8 8CD E CD œ O0- o O o rH rH

OiHK

T|4OHXOY

P4

b.

(W

Eo

Hi« H|M

O)

a(O

lO03

03 O CD iHO lO CD lO to tO<D CO O O 1 Ci rH•O o iH H r4 03

to O toO o CO to CD iHCi rH o o Ci 03•O iH iH rH 03

ci O to LO 03 rH lOK LO O LO CO 00 LO CD• •E tO lO lO CD CD lOü !> t- c

* 1 CD CO rH rH 00 rH 0)0> • rH to CD CD O CD CQrH OO O O Tt« C- lO O lOl»ü m rH H iH rH 03 to

• 1 03 CD 03 O O to o• • • •rH o to CD O o Ci t- CDÜ <D q O H iH 03 52O

m rH 03 to to CD a a

5<KOfeCOsRwp::

«

8CQg

89be expected.

At the other frequencies considered the vibration of the diaphragm w a s uniform over the whole field. As a check upon the validity of the results, the attenuation c oef fie lent was plotted against the square root ofthe frequency ( figure 32, page 90). The linear relationship between c< and Jjp" has been established by several workers (15) (IS) (17) (23) but there is disagreement over the magnitude of the slope of the graph which is proportional to the Helmholtz-Kirchhoff coefficient. The equation ,to the graph in figure 32 is

where r is the radius of the tube, c is the free gas velocity,

Pexp the experimental value of the Helmholtz- Kirchhoff coefficient.

The method of least squares gives the slope of the line as 6,05 X 10*^ cycle“^cm ^sec.^Now r = 5.71 cm.and c = 34,910 cm. sec.“^Hence

=: 0.681

The theoretical value of the Helmholtz-Kirchhoff coefficient t»e calculated as follov/s

90

t o

n

u_

t

iiuiiuwuaiMHMmininwi

91

!/ / \ / k \ VsLpT ' 4. (K-.)

where ^ =s coefficient of viscosity for the gas, j> — density of the gas,y = ratio of the principal specific heats of the gas Cp =: specific heat at constant pressure,K = thermal conductivity of the gas.

The values of the quantities in the above equation may be obtained as follows

? = I t X , 3 4 ,I ■* T . lo ’A

where T is the temperature in degrees absolute.Thus at 29.7®C.

Ç = 1.866 X 10" poise.

^ — j ^ cal.cra.~^sec." deg.C“ (24).% K z 6.327 X 10“ cal.cm. sec. deg.c

^ = 1.4019 (16 ) ( 17 )Cp 3. 0.241 cal.gm. ^deg.c (16)^ =: 1.166 X 10"3 gm.cm.~3

Thus^ 0.591

The excess is usually expressed as

l__Êl— X = 16 3 %Pr

THin . . i . . . , - r , . ' —o ,.-jiiiiiiijin iL ..n^... - - - - ,

92

Recent relevant results for this quantity are shown in table 4, page 93. It may be seen that there is general agreement that the experimental value of the Helmholtz-Kirchhoff coefficient is about 15-19^ higher than the theoretical value for smooth rigid walled tubes at lŒV frequencies.

Thus the agreement between the results of the present work and other work with air is sufficiently good to place confidence in the method and the further measurements with oxygen gas.

(b) Oxygen.The results obtained for the attenuation

coefficient using oxygen in the resonance tube are shavn in tables 5 - 1 0 , pages 94 - 99 . Observations using oxygen prepared by thermal decomposition of potassium permanganate are shown with an asterisk {^) after the value ofo(p in column 8. Column 5 gives the value of the water/oxygen molecular ratio calculated from the water vapour content. Column 6 gives the observed value of the attenuation coefficient and column 7 gives the value of the tube absorption calculated as follows:

Oo

l- iq 39.CÛ- rH 5 COiH( 1 to

CCL 1 1 •(V O CO CO 0- 05 lO< rH rH rH Oî O iH o 05 rH rHC£U 4* + + + f + + f +

G G« G Gef. o Oo to4J 1—1O • 03 03 • GE rH G oOS B 1 i G ü G G«r- 1 • ü o ü ü 03o G O O to 00tù o CO to 03 CO c- lO •rHO CO to o O to iH to to rH

G c C p; C•H •H •H •H •HG G G G G(D :3 :3 q d df iH m iH m rH rH m rH rH 1—!r* © w a m © © m © © ©

© © u © © © Pi B Pi-P :3 H 43 1—1 d d dro •o bO m •d bO •Ü "d 'ü

m © m m w mJ>s m \ \O ü ü o ü o üC m O O 'U o o o O<D \ o o q m o n o 03 o•- o o to W lO o to 03O* o O o© o iO rH to W rH q iH rH rHC lO 1 1 H O 1 W 1 1 1Cu o O 1 03 O 03 O O O

w o O O 1 O rH cg OV to lO to iH 2 rH rH rH

to to0]© GCO ©G .<■—' 03 X' ' G© © ©

§©JLjOJ © rH bO© A:

«y 3 torHrH cq 1- O s

© 03 O rH c8 to ?«w© AOO rH ÎZl m 05 43K Etq ©tQ

i © «a 1 •ürH 03 ©rH c©jj 43 t>> H B* iH © 43 m© O © 1 G Pi •H © Ü ©q5 H © © © Xi q #4 Pi

S K a w w CO (Xi

93

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HCOLiH

C O -

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finO:z;0MK<1O

m54

94

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X o

to 03 to O lO 0“O lO y5 ^ O O iH iH iH O O O Oo o o o o o o o o

iHO i iH •54 E •5J K o

.. . ■■ ■

t O l O i H i O t O l O r l O Ot Ô t O C D t O t D l D t O t O C DO O O O O O O O O

Tf tHO 1P- iH •X B

■a® ^ “

O C ^ ^ l ^ l O C O O S t H C O O0 ) r 4 H t C 0 O O ' f r - l % 3 '( D O - O O G O O t O C D t OO O O O O O O O O

lOs

XiX

O O O H c v : < X > ^ 0 3 l > - 0 • • • • • • • • •O C J t O C O l O t O r H O i t o to to O' 03 to CO 03 o H H rH 03 03

43C

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0 0 3 C O O » H 0 0 3 ' ^ t O • • • • • • * • •0 ' 5 j » t 0 0 < £ ) 0 t 0 0 > ‘0 r4 rH 03 03 03 to

© •d w ©© •© BPi opH

• • • • • • • • •^ ’ i O C ' i O : o “5 < O t O

& O© o54

t o 0 5 C O C O H r « O H « 0 C » * O 5 0 0 0 - r i > O 5 C 0 i H C 0 • • • • • • • • •0 5 0 > 0 > 0 5 0 > 0 5 0 i 0 0 > 03 03 03 03 03 03 03 t 0 0 3

g w © © 1 d 4-1 r4 #cr o o© >3 ©Pi o ro&i

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K B ^ « o• H C 0 5 * < O l O t O i O C O Q1 0 1 O 0 > 0 î O C 0 tJ « 0 > 0 >( M C V J t O l O t O O î C J O OO O O O O O O O O

rH3

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f H c v j t D O O O > C D I > - O lO iH iH q O O O O O O 0 5 0 ) 0 ( X > 0 > C 0 0 5 G > 0 >O O o o O O O O o

^ rHq 1pj rH •% G © K O0

N O o q o î ' H w c o i d ^ l < | > - Q r H ^ C O u 3 o > 0 5 i H i H t O O I O J r H i H O i O • • • • • • • • *r H i H i H r H f H r H i H O O

ips

XiH

O C 0 r H c \ l C 0 ' r f ( M l > O • • • • • • • • •O O l t O C O l O i O M O y o t O l O f - O ï t O C O C M C '

iH iH iH 03 03

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rj» t o CD CD 05 rj» t O C O O rH CQ rH rH rH rH C M r H r H

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r j t O O b ' O O O l O l Ob - t O b - t O D O ^ O r j »

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IPorH

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10 108 8

to b- 0 0 8 0 0 0 0GO 05 ’M» 0 GO rj» 05 rj»rj» CO CO GO 0 rj» to %> C'CM CM CM CM to to rj» to CM

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«M» t o CO 0 0 O) rj» t o 0 0 0 5rH CM « H rH rH rH CM rH rHrH rH rH rH rH rH rH rH rHt o t o t o tO t o t o t o t o t o

b> 10 D 0 0 to CMGO rH 0 05 Tj» to CM05 0 rH 05 05 05 CM00 05 05 GO GO GO 05rH rH rH rH rH rH rHrH rH rH rH rH rH rH

OrHg9E»

where

100

n =r — ^ ----- X poi^e (24)f I 4- ^

T. loVr

Si 2 #09 X 10"^ poise J Ü 1.282 X 10-3 gm.CTn.-3X = 1.400 (30)

T» lo ' cal.cm.-^sec.*^deg.c^(24)

= 5.47 X 10 cal.cm.*^sec .- deg.c*C =0.219 cal.deg.flgm.-l (25)C =33,160 c m . s e c . (30)

Hence=0.596

This value of^rp must be increased by 15.3% in accordance with the earlier results.Hence

= 0.688

0.646 X 1 0 cm."^

This value ofO rp has been corrected for pressure dependence in column 7. The difference between columns 6 and 7 is presented in column 8 as the contribution towards the absorption coefficient due to the relaxation process.

The above procedure was necessary in order to

101allow for the relaxation absorption that has been observed by some workers (31) (32) (33) in dry oxygen.

The values of the relaxation absorption are plotted against the molecular ratio h in figures 33 - 38, pages 102 - 104 . These graphs indicate that at a particular frequency the absorptionshows a maximum at a certain value of h. Also the magnitude of the maximum value of

increases as the frequency increases and further, the value of h at which maximum absorption occurs, increases with frequency.

Figure 39, page 105 shows the value of the maximum absorption ( p )mgx plotted against the frequency f. This is a straight line in agreement with the theory and also with the results obtained by Knotzel (14) at higher frequencies. A value of Cj the specific heat of vibration may be obtained from the slope of figure 39 and equation page 22 .

irCLSlope of figure 39 =

= (1.80 0.08 ) X 10"^ cycle.-1cm.-Isec.

Thus (0.0332 ^ 0.0015)R

This result compares very favourably with the result of Smith and Tempest (31) who obtained (0.034 i. 0.003)R with dry oxygen and also the value of 0.0339R calculated from spectroscopic data.

102

cr

c*

•o

COo

uo

oXX

2 7.s

'!ÿ

"o

5

103

VD

m

O

cvi

T

104

oocOw

U.

u_

VO2O X

S -C

rtI

105

(X

oo

Oo

: yo mwjo7 -J

OOoo

ao

'7~OtU)00'a)(/IL

OOJ-

OON

Oél

lermwimnbWiwwwimwe

106

The frequency of maximum absorption is plotted against the water/oxygen molecular ratio in figure 40, page 107* The errors involved here are clearly larger than those in figure 39 since the latter depend upon the precision in measuring oC and the former upon the humidity measurement which was rather more uncertain. A direct comparison with other workers is not possible because these are the first measurements made at low frequencies. However there is little agreement among other workers over the relation between f^ax and h at higher frequencies and some of the more reliable curves are shwvn in figure 40, page 107, extrapolated to the low frequencies used in this work. The best fit curve to the present work was calculated to be

>8v,2 -1max = 2.1 X 10 h 4" 1.20 X 10 h cycle, sec.

It is now necessary to consider the purity of the oxygen used in this work in order to assess the reliability of the results. The cylinder oxygen contained several impurities listed on page 84 of which the carbon dioxide and any water vapour were removed by the purifying system. The remaining impurities which could have an effect upon the absorption coefficient and relaxation time were hydrogen (<50 v.p.m.) and acetylene or benzene (<10 v.p.m.). However according to the work of Knudsen (10) the very small quantities present in this work would have negligible effect upon the results.

107

\ooO

f

h X \ûFRG.<^üE.KC OF MAXIMUM

B^Sof^FTVoK Ç^&FkiMST K F o ( \ OM<^E.k

10 B

The oxygen prepared by thermal decompositionof potassium permanganate had impurities amounting to

'7less than 2 parts in 10 which were considerably smaller than the amounts observed to produce a decrease in the relaxation time by Knudsen. Further confirmation that impurities other than water vapour did not contribute to the absorption was given by the consistency between the absorption coefficients obtained using oxygen prepared by two entirely different methods.

Thus the quadratic dependence of the frequencyt

of maximum absorption upon the moisture content has been established at I w frequencies and general agreement obtained with extrapolated results of other workers at higher frequencies.

•»»«»oo0oO““*“

109

CHAPTER 11.

DISCUSSION OF THE METHOD.

The theoretical basis of the method for measuring the sound velocity and attenuation has been investigated by Harlow (16). The effects of imperfect reflection of the sound wave at the reflector, slip, relative radial motion at the tube wall and finite thermal conductivity of the walls were considered and shown to give rise to negligible effects in the apparatus.

The technique for estimating the impedance has been improved to enable the method to be used for diaphragms of larger diameter where the natural frequency is lav and the impedance not necessarily linear between the anti-resonant frequencies. The validity of this technique has been demonstrated by the close agreement between the results obtained here and previous work using air at law frequencies.

The chief inaccuracy in the work with oxygen was in the measurement of the moisture content of the gas. Much previous work has been open to the criticism that the extent of the disturbance by impurities has been unknown. Havever, in this work, the close agreement between the results using oxygen prepared by two entirely

110different methods, has established the freedom from impurity effects.

The moisture content was measured in the most direct manner possible by introducing a known weight of water and after the observations pumping it off and absorbing. The agreement between the quantity entering and leaving was in most cases very good. Any discrepancies which did occur were probably due to an adsorbed film of moisture upon the walls of the resonance tube.

Thus the investigation into the dependence of the attenuation of sound upon frequency has been extended to very low frequencies and lov; moiàture contents in oxygen and has been shavn to yield good general agreement with the theory of relaxation. The frequency of maximum absorption of sound waves in oxygen has been shown to be a quadratic function of the water vapour/oxygen molecular c oneentrâtion.

Finally the value obtained for the vibrational specific heat of oxygen has been shovn to be in close agreement with the value calculated from spectroscopic data.

———o oO00———

Ill

appendix.

EXPERIMENTAL PROCEDURE AND SPECIMEN CALCULATION.

The thermostat system was reliable enough to be able to be left operating over long periods without attention. Consequently observations could be made on any day of the week and long periods of waiting for steady conditions were avoided.

The following notes indicate the procedure adopted for the absorption coefficient determination at the sixth mode of vibration of the gas column on Friday 13/10/61.

Tuesday 10/10/61.The furnace was charged with 1 Kgm. Analar Grade

potassium permanganate, evacuated and heated to 150^0. for 48 hours. The resonance tube was flushed slavly with cylinder oxygen.

Thursday 12/10/61.The temperature of the furnace was raised to

200°C. and the resonance tube was flushed with pure oxygen for 3 hours at a rate of approximately 200 cc./min. The gas flow was then diverted through a side tube containing

11228.0 mgm. of distilled water weighed out in a small boat. After the water had evaporated, the gas was passed for a further 15 minutes to ensure that all the water vapour passed into the resonance tube which was then isolated by- turning off the inlet and exit taps. The drying tavers at the exit from the resonance tube were weighed before •and after the introduction of the water vapour but no Increase of weight was observed. The system was then allowed to come to equilibrium overnight. The RC oscillator was switched on and allowed to stabilise overnight.

Friday 13/10/61,The time switch started the stirrers and fan

at 7.00 a.m. The temperatures indicated by the four thermometers were within the required limits of 0.02®C. by 11.00 a.m. The temperatures recorded during the day were as follov/ss

Thermometer11.00 a.m.4.00 p.m.

Mean Temperature *C.Corrected Temperature (using N.P.L. certificate)

against the B.B.C. 200 Kcycle. sec."^ transmission and gave

1 2 3 431.06 31.08 31.12 31.1031.06 31.10 31.11 31.0931.06 31.09 31.11 31.0931.12 31.13 31.15 31.15

• standard Was checked

113

100 beats in 50 sec. This gave the standard frequency as100,001.0 cycle. sec.“^

The pressure of the gas in the resonance tube was determined using a manometer and Fortim barometer. This gave the pressure of the gas in the tube as 77.48 cm. Hg.

The piston at the reflector was then screwed up to complete the plane reflecting surface. The optical system had previously been set up to give the interference fringes and did not have to be disturbed during filling or flushing.

The amplifiers were switched on, the phonic motors were started and the currents required to produce the first disappearance of the fringes at frequencies near the chosen resonance, were measured. To ensure greater accuracy the fan and stirrers were switched off from inside the darkroom during the final adjustment of the decade resistance box. The camera box was mounted in the darkroom alongside the observer and the photographs of the revolution counters were taken before and after the setting of the current corresponding to a particular frequency. The time interval between photographs was approximately one minute.

Critical current determinations were made at 18 frequencies separated by 0.4 cycle, sec.” in the neighbourhood of the sixth mode of the resonance tube at approximately 598 cycle, sec."^ The experimental

114observations are shown in table 11, page 115*

When the observations had been completed the resonance tube was flushed out for 24 hours with dry cylinder oxygen* The increase of weight of the absorbing towers was;

mgm,1^ tower 26.82^^ tower 0.2 mgm.Total 27.0 mgm.

Mean moisture content 27.5 mgm.

The impedance curve was then plotted from the observations and is shown in figure 41, page 116, from which the circle diagram figure 4 2 page 117, was derived exactly as described on page30 using an estimate of 11.25 units for Z^. Eleven values of on the circle diagram were selected near resonance and the corresponding values of Zqq and frequency were deduced from the circle diagram and impedance curve. A graph of tan against frequency was drawn and is shown in figure 43, page 11&. The graph proved to be a straight line establishing the correctness of the estimate for Zq. From the slope and intercept of the tan cj) against f graph:

s = 0.334 cycle“^sec.

N

Now

fw =: 598.0 cycle. sec.“^

=r 167.810 cm.

NO.cR iTKflU CURRENTUNITS.

U PPER CourrrER

L owe-R coo MT61

uTPe-RJ>\FF.

Lowe-R PRSQUENCX CYCLE, sec"*

_____Z '^ 0 o

56 5.07

50907.67852024.168

21547.78623404.942 1116.490 1857.156 601.183 8.43

78 4.98

52388.355 53605.6 92

24010.81226037.168 1217.337 2026.356 600.752 8.29

910 4.93

53917.02555224.370

25 555.452 28732.528 1307.345 2177.076 600.505 8.20

1112 4.93

55474.965 56 752 . 982

29149.87731279.233 1278.017 2129.356 600.189 8.22

1314 4.97

57067.36758087.463

31803.10233503.952 1020.096 1700.850 599.757 8.28

1516 5.08

58466.77761498.339

34136.48839193.912 3031.562 5057.424 599.428 8.48

1718 5.33

61811.76763071.604

39716.88041820.212 12 59.837 2103.332 598.972 8.90

1920 5.70

63352.19064513.475

42288.73444228.952 1161.285 1940.218 598.533 9.52

2122 5.92

6 4769.676 6 5552.6 78

44657.04445965.863 783.002 1308.819 598.251 9.90

2324 6.20

6 5922.651 66 968.6 44

46584.34548333.605 1045.993 1749.260 597.963 10.37

2526 6.51

67226.78467905.909

4876 5.362 49901.794 679.125 1136.432 597.594 10.88

2728 6.85

6826 4.073 69576.335

50501.198 526 98.66 7 1312.262 2197.469 597.170 11.47

2930 7.09

69862.79371265.565

53178.40255528.720 1402.772 2350.318 596.843 11.87

3132 7.55

71495.38272346.808

55913.90157343.092 851.426 1429.191 595.740 12.67

3334 7.60

7266 5.827 73102.580

57878.66258612.685 436.753 734.023 595.013 12.78

3536 7.61

73305.52774631.179

58953.92561186.096 1325.6 52 2232.171 593.885 12.81

3738 7.58

74852.68475439.179

61559.12262547.455 586.495 988.333 593.418 12.78

3940 7.37

75616.590 75846.930

62846.53263235.350 230.340 388.818 592.411 12.44

t a b l e I I .

116

Q.

5CL

O <x>

wtp

r(joO'uJ0U-

'SXiViO

117

F i g u r e S-2. c i r c u e D ir& r r h 13

118

u-

O

H"Z(XU)<x-a-Tcrh

SuiCCOü»

-G-iH

119and

N = 6Thus

^ “ = 5.62 X 10"4 cm."^

——"OoOoO"—"

120

REFERENCES.

The titles of periodicals are abbreviated in accordance with the World List of Scientific Periodicals Published in the Years 1900 - 1950 , Third Edition,Butterworth’s Scientific Publications, London 1952.

(l)Stokes,G.G. Trans.Camb.phll.Soc• 8 287 (1845)(2 )Kirchhoff,G. Ann.Phys.,Lpz. 134 177 (1868)(3 ) Lamb ,H. The Dynamical Theory of Sound. 263 (1925)(4)Jeans,J.H. The Dynamical Theory of Gases. 374 (1904)(5)Herzfeld,K.F.

& Rice,F.O.Phys.Rev. 691 (1928)

(6 )Kneser,H.O. J.acoust.Soc .Amer. 5 122 (1933)(7)Knudsen,V.O. J.acoust.Soc.Amer. 5 126 (1931)(8 )Chrisler,V.L.

& Miller,C.E.J.Res.nat.Bur.Stand. 9 175 (1932 )

(9)Knudsen,V.O. J.acoust.Soc.Amer. 5 112 (1932)(10)Knudsen,V.O. J.acoust.Soc.Amer. 6 199 (1935 )(ll)Kneser,H.O.

& Knudsen,V.O.Ann.Phys. ,Lpz. 413 682 (1935)

(12)Knudsen,V.O. & Obert ,L.

J.acoust.Soc.Amer. 7 249 (1936 )

(13)Knotzel,H. Akust.Z. 5 245 (1940)

121

14)Knotzel,H.& Knotzel,L.

Ann.Phys.,Lpz. 437 393 (1948)

15 )Reay ,W.W. M.Sc.Thesis,London University. (1950)16)Harlow,R.Q. Ph.D.Thesis,London University. (1954)17)Smith,D.H.

& Harlow,R.G.To be published.

18)Smith,D.H. Proc .phys.Soc .Lond. 534 (1945)19)Noltingk,B.E.

& Snelling,M.AJ.sci.Instrum. 349 (1953 )

20)Goodman,W. Heat.Pip.Air Condit. 10 119 (1938)2l)Scott,R.B. The Measurement and Control of 206

Temperature in Science and Industry.(1941)

22)Hoge,H.J. J.Re3.nat.Bur.Stand. àà 321 (1950)23 )Lawley ,L.E. Proc.phys.Soc.Lond. B65 181 (1952 )24)Keyes,F.G. Trans.Amer.Soc.mech.Engrs. 73 589 (1951)25)Spencer,H.M. J.Am.Chem.Soc. 67 1859 (1945 )26 )Waet zmann,E.

& T7enke,W,Akust.Z. ± 1 (1939)

27)Lawley ,L.E. Proc.phys.Soc.Lond. B67 65 (1954)28)Kemp,G.T.

& Nolle ,A.W.J.acoust.Soc.Amer. 25 1083 (1953)

29)Lee,T.A. Ph.D.Thesis,London University. (1958)30)Wintle,H.J. M.Sc.Thesis,London University. (1959)31)Smith,F.A. J.ac oust.Soc.Amer. 33 1626 (1961)

& Tempest,W.32 )Parker, J.G. J.chem.Phys. M 1763 (1961)33)Henderson,M.C. J.acoust.Soc.Amer. 349 (1962)34)Shields,F.D.& J.acoust.Soc.Amer. 29 470 (1957)

Lagemann.R.T

222

I wish to express my thanks to the Governing Body, Principal and Head of the Physics Department of the Battersea College of Technology for providing facilities for the research and to the Department of Scientific and Industrial Research for providing a grant, I am also very grateful to Dr. R.G. Harlow for suggesting the problem and offering encouragement and to my wife for assistance in the preparation of the typescript and figures.

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