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

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.

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.

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!

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.

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.

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

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,

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

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.

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

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

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);

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.

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.

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

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

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

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

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

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

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:

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

CONCLUSION: Chapter 22CONCLUSION: Chapter 22Sound WavesSound Waves