chapter 22a – sound waves a powerpoint presentation by paul e. tippens, professor of physics...
TRANSCRIPT
![Page 1: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/1.jpg)
Chapter 22A – Sound Chapter 22A – Sound WavesWaves
A PowerPoint Presentation byA PowerPoint Presentation by
Paul E. Tippens, Professor of Paul E. Tippens, Professor of PhysicsPhysics
Southern Polytechnic State Southern Polytechnic State UniversityUniversity© 2007
![Page 2: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/2.jpg)
Objectives: After completion of Objectives: After completion of this module, you should be this module, you should be able to:able to:
• Define Define soundsound and solve and solve problems relating to its velocity problems relating to its velocity in solids, liquids, and gases.in solids, liquids, and gases.
• Use boundary conditions to Use boundary conditions to apply concepts relating to apply concepts relating to frequenciesfrequencies in in openopen and and closedclosed pipes.pipes.
![Page 3: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/3.jpg)
Definition of SoundDefinition of Sound
Source of sound: Source of sound: a tuning fork.a tuning fork.
SoundSound is a is a longitudinal longitudinal mechanical wave mechanical wave that travels through that travels through an elastic medium.an elastic medium.
SoundSound is a is a longitudinal longitudinal mechanical wave mechanical wave that travels through that travels through an elastic medium.an elastic medium.
Many things vibrate Many things vibrate in air, producing a in air, producing a sound wave.sound wave.
![Page 4: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/4.jpg)
Is there sound in the Is there sound in the forest when a tree falls?forest when a tree falls?
Based on our definition, Based on our definition, there there ISIS sound in the sound in the forest, whether a human forest, whether a human is there to hear it or not!is there to hear it or not!
Sound is a Sound is a physical physical disturbancedisturbance in an in an elastic medium.elastic medium.
Sound is a Sound is a physical physical disturbancedisturbance in an in an elastic medium.elastic medium.
The elastic medium (air) is required!
![Page 5: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/5.jpg)
Sound Requires a MediumSound Requires a Medium
Evacuated Bell Jar
Batteries
Vacuum pump
The sound of a ringing bell diminishes as air The sound of a ringing bell diminishes as air leaves the jar. No sound exists without air leaves the jar. No sound exists without air molecules.molecules.
![Page 6: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/6.jpg)
Graphing a Sound Wave.Graphing a Sound Wave.
Sound as a pressure wave
The sinusoidal variation of The sinusoidal variation of pressurepressure with with distancedistance is a useful way to represent a sound is a useful way to represent a sound
wave graphically. Note the wave graphically. Note the wavelengthswavelengths defined by the figure.defined by the figure.
![Page 7: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/7.jpg)
Factors That Determine the Speed of Factors That Determine the Speed of Sound.Sound.
Longitudinal mechanical waves (Longitudinal mechanical waves (soundsound) have a ) have a wave speed dependent on wave speed dependent on elasticityelasticity factors and factors and densitydensity factors. Consider the following examples: factors. Consider the following examples:
A A denserdenser medium has greater medium has greater inertia resulting in inertia resulting in lowerlower wave wave speeds.speeds.
A medium that is A medium that is more elasticmore elastic springs back quicker and springs back quicker and results in results in fasterfaster speeds. speeds.
steelsteel
waterwater
![Page 8: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/8.jpg)
Speeds for different mediaSpeeds for different media
Yv
Metal rodMetal rod
Young’s modulus,Young’s modulus, Y Metal density,Metal density,
43B S
v
Extended Extended SolidSolid
Bulk modulus,Bulk modulus, B Shear Shear modulus,modulus, S Density,Density,
Bv
FluidFluid
Bulk modulus,Bulk modulus, B Fluid density,Fluid density,
![Page 9: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/9.jpg)
Example 1:Example 1: Find the speed of Find the speed of sound in a steel rod.sound in a steel rod.
vs = ?
11
3
2.07 x 10 Pa
7800 kg/m
Yv
v =5150 m/s
== 7800 kg/m7800 kg/m33
Y =Y = 2.07 x 102.07 x 1011 11 PaPa
![Page 10: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/10.jpg)
Speed of Sound in AirSpeed of Sound in AirFor the speed of sound in air, we find that:For the speed of sound in air, we find that:
P RT
B P andM
= 1.4 for air R = 8.34 J/kg mol M = 29 kg/mol
B Pv
RT
vM
Note: Sound velocity increases with Note: Sound velocity increases with temperature T.temperature T.
![Page 11: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/11.jpg)
Example 2:Example 2: What is the speed of What is the speed of sound in air when the temperature sound in air when the temperature is is 202000CC??
-3
(1.4)(8.314 J/mol K)(293 K)
29 x 10 kg/mol
RTv
M
Given: = 1.4; R = 8.314 J/mol K; M = 29 g/mol
T = 200 + 2730 = 293 K
M = 29 x 10-3 kg/mol
v = 343 m/sv = 343 m/s
![Page 12: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/12.jpg)
Dependence on Dependence on TemperatureTemperature
RTv
M
RTv
M
Note: Note: vv depends on depends on
Absolute TAbsolute T::Now v at 273 K is 331 m/s. , R, M do not do not change, so a simpler change, so a simpler formula might be:formula might be:
T331 m/s
273 Kv
Alternatively, there is the approximation using Alternatively, there is the approximation using 00C:C:
0
m/s331 m/s 0.6
C cv t
![Page 13: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/13.jpg)
Example 3:Example 3: What is What is the velocity of sound the velocity of sound in air on a day when in air on a day when the temp-erature is the temp-erature is equal to 27equal to 2700C?C?
Solution 1:Solution 1:T
331 m/s273 K
v
300 K331 m/s
273 Kv T = 270 + 2730 = 300 K;
v = 347 m/sv = 347 m/s
v = 347 m/sv = 347 m/sSolution 2:Solution 2: v = 331 m/s + (0.6)(270C);
![Page 14: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/14.jpg)
Musical InstrumentsMusical Instruments
Sound waves in air Sound waves in air are produced by the are produced by the vibrations of a violin vibrations of a violin string. Characteristic string. Characteristic frequencies are based frequencies are based on the length, mass, on the length, mass, and tension of the and tension of the wire.wire.
![Page 15: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/15.jpg)
Vibrating Air ColumnsVibrating Air ColumnsJust as for a vibrating string, there are characteristic wavelengths and frequencies for longitudinal sound waves. Boundary conditions apply for pipes:
Open pipeA A
The open end of a pipe must be a displacement antinode A.
Closed pipeAN
The closed end of a pipe must be a displacement node N.
![Page 16: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/16.jpg)
Velocity and Wave Frequency.Velocity and Wave Frequency.
The period T is the time to move a distance of one wavelength. Therefore, the wave speed is:
1 but so v T v f
T f
The frequency f is in s-1 or hertz (Hz).
The velocity of any wave is the product of the frequency and the wavelength:
v f v
f
![Page 17: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/17.jpg)
Possible Waves for Open Possible Waves for Open PipePipe
L 2
1
L Fundamental, n = 1
2
2
L 1st Overtone, n = 2
2
3
L 2nd Overtone, n = 3
2
4
L 3rd Overtone, n = 4
All harmonics are possible for open pipes:
2 1, 2, 3, 4 . . .n
Ln
n
![Page 18: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/18.jpg)
Characteristic Frequencies Characteristic Frequencies for an Open Pipe.for an Open Pipe.
L 1
2
vf
LFundamental, n = 1
2
2
vf
L1st Overtone, n = 2
3
2
vf
L2nd Overtone, n = 3
4
2
vf
L3rd Overtone, n = 4
All harmonics are possible for open pipes:
1, 2, 3, 4 . . .2n
nvf n
L
![Page 19: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/19.jpg)
Possible Waves for Closed Possible Waves for Closed Pipe.Pipe.
1
4
1
L Fundamental, n = 1
1
4
3
L 1st Overtone, n = 3
1
4
5
L 2nd Overtone, n = 5
1
4
7
L 3rd Overtone, n = 7
Only the odd harmonics are allowed:
4 1, 3, 5, 7 . . .n
Ln
n
L
![Page 20: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/20.jpg)
Possible Waves for Closed Possible Waves for Closed Pipe.Pipe.
1
1
4
vf
LFundamental, n = 1
3
3
4
vf
L1st Overtone, n = 3
5
5
4
vf
L2nd Overtone, n = 5
7
7
4
vf
L3rd Overtone, n = 7
Only the odd harmonics are allowed:
L
1, 3, 5, 7 . . .4n
nvf n
L
![Page 21: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/21.jpg)
Example 4.Example 4. What What lengthlength of of closed closed pipe is pipe is needed to resonate with a fundamental needed to resonate with a fundamental frequency of frequency of 256 Hz256 Hz? What is the ? What is the second second overtoneovertone? Assume that the velocity of ? Assume that the velocity of sound is sound is 340 M/s340 M/s..
Closed pipeAN
L = ?
1, 3, 5, 7 . . .4n
nvf n
L
11
(1) 340 m/s;
4 4 4(256 Hz)
v vf L
L f L = 33.2 cm
The second overtone occurs when n = 5:
f5 = 5f1 = 5(256 Hz) 2nd Ovt. = 1280 Hz2nd Ovt. = 1280 Hz
![Page 22: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/22.jpg)
Summary of Formulas For Summary of Formulas For Speed of SoundSpeed of Sound
Yv
Solid rod
43B S
v
Extended Solid
Bv
Liquid
RTv
M
Sound for any gas:
0
m/s331 m/s 0.6
C cv t
Approximation Sound in Air:
![Page 23: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/23.jpg)
Summary of Formulas Summary of Formulas (Cont.)(Cont.)
vf
vf
v f For any wave:
Characteristic frequencies for open and closed pipes:
1, 2, 3, 4 . . .2n
nvf n
L 1, 3, 5, 7 . . .
4n
nvf n
L
OPEN PIPE CLOSED PIPE
![Page 24: Chapter 22A – Sound Waves A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University © 2007](https://reader033.vdocuments.us/reader033/viewer/2022061406/56649eec5503460f94bfd6ca/html5/thumbnails/24.jpg)
CONCLUSION: Chapter 22CONCLUSION: Chapter 22Sound WavesSound Waves