III. ANALYSIS

Sound moves by unlikely speeds depending on medium it travels

through. Of the three mediums (solid, liquid, and gas) sound waves travel

the slowest through gases, faster through liquids, and fastest through solids.

It travels fastest through solid since its molecules are much bonded together

compared to liquid and gas. Temperature also affects the speed of sound.

When a person hits, strikes, strums, plucks or somehow disturbs the

object, musical instruments are set into vibration motion at their natural

frequency. Each natural frequency of the object is associated with one of

the many standing wave patterns by which that object could vibrate. The

natural frequencies of a musical instrument are sometimes referred to as

the harmonics of the instrument. An instrument can be forced into vibrating

at one of its harmonics (with one of its standing wave patterns) if

another interconnected object pushes it with one of those frequencies. This

is known as resonance, when one object vibrating at the same natural

frequency of a second object forces that second object into vibrational

motion.

Kundt’s tube was invented in 1866 by German physicist August

Kundt for determining the speed of sound through different mediums. It is

used representing standing waves and acoustical forces today. The tube has

little quantity of fine powder such as cork dust, talc or Lycopodium

(Lycopodium was used in this experiment), which is visible since the tube is

transparent. Kundts utilized metal rod resonator for vibration before, but

modern demonstration generally use a loudspeaker attached to a signal

generator which produce a sine wave. The other end of the tube is enclosing

by a changeable piston which can be used to adjust the length of the tube.

Thus the velocity of any wave is given by:

v = f λ

where: v is the velocity, f is the frequency, λ is the wave length

The tube signifies that is at resonance when the sound generator is

turned on and changed in anticipation of the sound gets much loader. This

indicates that the tube is at resonance. The distance of the round-trip path of

the sound waves, from one end of the tube to the other and back again, is a

multiple of the wavelength λ of the sound waves. Hence, the length of the

tube is a multiple of half a wavelength. The sound waves in the tube are in

the form of standing waves, and the amplitude of vibrations of air is zero at

equally spaced intervals along the tube, called the nodes. The powder is

caught up in the moving air and settles in little piles or lines at these nodes,

because the air is still and calm there. The distance between the piles is one

half-wavelength λ/2 of the sound. By measuring the distance between the

piles, the wavelength λ of the sound in air can be found. If the frequency f of

the sound is known, multiplying it by the wavelength gives the speed of

sound c in air. The speed of sound in air can be determined by measuring the

air temperature t in Celsius degree:

vair = 332 m/s + 0.6(t)

where: vair is the velocity in air, t is the temperature in Celsius

The frequency of the sound in the air is the same as that in the metal

rodf rod, that is f air =f rod. Thus, this frequency can be used to calculate the

speed of wave in metal given by

vr = vaLrLa

where: vr is the velocity of the rod, va is the velocity of air, Lr is the

length of rod, and La average length of powder segment

The velocity of sound in a solid rod is given by

vr = √Yρwhere: vr is velocity of the rod, Y is the Young’s modulus of the rod,

ρ is the density of the rod

In this experiment Kundt’s Tube Apparatus, a meter stick, a piece of

cloth, a thermometer, rosin and Lycopodium powder will be used. The

Kundt’s tube consists of a long, narrow glass tube mounted in a metal frame

case. A metal rod (any desired material) is clamped in such a way that its

end containing the disk is inside the tube. The rod can be clamped at any

distance. However, it is better to clamp it at the center to make the

experiment not complicated. The Kundt’s tube is closed at one end by a

stopper.

(Materials Used)

The first picture shows the rod is pulled toward the end of the rod to

produce vibration.

The photo above shows that we measures the distance of successive

powder heaps. All the lengths needed in this experiment are measured using

the meter stick. A low accuracy instrument is just fit with the experiment

because it is not important to measure accurate lengths. Finally,

thermometers are the instrument used in measuring the temperature of the

room. Normally, we have to put the powder inside the glass tube. But in the

experiment, it is already prepared by the laboratory assistants to prevent

waste of materials.

The powder is evenly distributed throughout the tube. It is done to

make the wave visible later, that is in similar shapes and sizes. The kind of

material where the rod is made is to be recorded. The value of the constants,

Y and ρ, for the specific material used are obtained using any form of

resources. Furthermore, the length of the tube is to be measured using a

meter stick. We carefully adjusted if the rod is clamped horizontally at its

center. This allows the experiment performer to easily calculate the value of

velocity of the rod. The rod has a disk at its one end inside the tube. This

disk has not to touch the walls of the glass tube. It must be leave free to

vibrate. Also, it should be necessary to measure and record the temperature

of the room, inside the tube or near the apparatus itself.

After the preliminary assessment of the apparatus, we proceed on

vibrating the rod. The rosin is initially rubbed on the cloth. The rosin allows

the cloth to produce friction with the tube. The energy due to friction will

serves as a wave. Strokes on the rod are done after wards. It is ideal to do

smooth, high-pitch tone stroke in a lengthwise manner. It is important not to

let the hand slip off at end of the rod. This is because, it causes both ends of

the rod to vibrate transversely, and the vibrating disk may break the glass

tube.

When the dust inside the tube does not form visible waves, it is

advised to adjust the air column by moving it towards the tube in a minimal

distance. Continual adjustment can be made until best resonance condition is

achieved. This happens when dust agitated formed perfect waves which are

measurable and looks exactly the same from one another. When the rod gets

warmed greatly, we could cease the stroking and let it cool for a while.

Another problem encountered in this experiment is when one observed that

majority of the dust is concentrating on one side of the node. This can be due

to the apparatus is not oriented horizontally. We can minimize this problem

by removing some dust.

Once the visible waves formed, we proceed on measuring the length

of the waves (wavelength). On measuring, the first dust loop nearest to the

disk of the rod is neglected. It is an option to measure one, two, three or any

number of waves desired. However, it is more accurate to measure many

waves. From the measured distance, we determined the average half

wavelength of the sound in air column, La, by dividing it to the total number

of loops or segments measured. We calculate for the velocity of sound in air

at the temperature recorded earlier. Once done, solve for the value of the vr.

From the table of velocity of sound in solid in the textbook, we compared

the obtained experimental value with the theoretical value.

In the experiment, the group had accomplished the objective of the

experiment which determine the velocity of sound in metal rod and

determine the speed of sound in the tube applying the principles of

resonance. The wave produced in Kundt's tube follows the wave behavior of

the close type case. In vibrating the rod, energy comes from the friction

produced by stroking cloth at the rod. To produce friction, rosin is rubbed in

the cloth. The wave’s produced inside after vibration is visibly seen through

agitation of Lycopodium powder.

Table 1. Kundt’s Tube: Velocity of Sound in Solid

Length of metal rod Lr 91.5 cm

Average length of powder segments

La

8.75 cm

Temperature of air t 22 °C

Velocity of Sound in air va 345.2 m/s

Velocity of sound in the rod vr 3609.81 m/s

Velocity of sound in the rod vr 3475 m/s

Percentage Error % 3.88 %

Density of the rod ρ 8440 kg/m^3

Velocity of sound in the rod vr 3283.59 m/s

Percentage Error % 5.51 %

Based on the table above, the velocity of sound produce in the rod can

be computed using equation the equation: vr = vaLrLa

since the frequency of

the sound in the air is the same as that in the metal rod. The velocity of

sound computed can be obtained using the equation: vr = √Yρ using young's

modulus and density of the rod. Possible error encountered in this

experiment is when the majority of the dust is concentrating on one side of

the node. This can be due to the apparatus is not oriented horizontally.

IV. CONCLUSION

The second type of mechanical wave which longitudinal waves were

the velocity of the wave is parallel to the movement of particle. An example

of longitudinal wave is sound wave. For this experiment, the velocity of

sound in the rod and tube were determined.

The velocity of sound in rod depends on two things, the air

temperature, length and type of rod. First, high temperature permits sound to

travel faster. From the velocity of sound in air, a proportion was observed

that velocities of sound in rod and in air are indirectly proportional to the

average length of the successive heaps and length of the rod, respectively.

Hence, smaller ratio between lengths of the rod to the average length

successive powder heaps will produce higher value of the velocity.

Another factor that affects the velocity of sound in rod is its ability to

expand or the Young’s Modulus and the inertia resisting the return to

equilibrium, or the density. Velocity of sound is found to be directly

proportional to the square root of Young’s Modulus and indirectly

proportional to the square root of density. Thus, higher young’s modulus

will give higher velocity of sound and higher value of density will give low

value of velocity.

The experiment aims to determine the velocity of sound in metal rod

and determine the speed of sound in the tube applying the principles of

resonance. The velocity of sound can be determined using Kundt’s tube

apparatus. Using the principles of resonance and applying the velocity of

wave, the group computed the value of the velocity of sound in the rod vr

(computed) was 3283.59 m/s with a 5.51 % error compared to velocity of

sound in the rod vr (textbook) which is equal to 3475 m/s. These proves that

the velocity of the sound can be computed through applying principles of

resonance and verified that sound travels through the air and rod as its

medium and behaves longitudinal waves.