SOUND WAVESSound is a longitudinal wave produced by a vibration that travels away from the source through solids, liquids, or gases, but not through a vacuum. The speed of sound is independent of the pressure, frequency, and wavelength of the sound. However, the speed of sound in a gas is proportional to the temperature T. The following equation is useful in determining the speed of sound in air

v = 331 + 0.6 T Units: m/sWhere 331 is the speed of sound in m/s at 0°C, and T is the temperature in °C

The speed of sound is different in different materials. The speed of sound in air at room temperature (20ºC) is 343 m/s.

There are two main characteristic of sound: pitch and loudness.

Pitch refers to how high the sound is. It is measured by thefrequency. The higher the frequency the higher the pitch. Thelower the frequency the lower the pitch.

We hear frequencies in the range of 20 Hz to 20,000 Hz.This is called the audible range.Frequencies above this range are called ultrasonic.Sound waves whose frequency is lower than the audible range are called infrasonic.

HUMAN EAR:The ear consists of three basic parts:

Outer ear: serves to collect and channel sound to the middle ear.

Middle ear: serves to transform the energy of a sound wave into the internal vibrations of the bone structure of the middle ear and transform these vibrations into a compressional wave in the inner ear.

Inner ear: serves to transform the energy of a compressional wave within the inner ear fluid into nerve impulses which can be transmitted to the brain.

Hearing:

A compression forces the eardrum inward and a rarefaction forces the eardrum outward, thus vibrating the eardrum at the same frequency of the sound wave.

SOURCES OF SOUND

Sound comes from a vibrating object. If an object vibrates with frequency and intensity within the audible range, it produces sound we can hear.

MUSICAL INSTRUMENTS

- String Instruments: guitar, violin and piano

-Wind Instruments:

Open Pipe: flute and some organ pipes

Closed Pipe: clarinet, oboe and saxophone

STRING INSTRUMENTSThe sounds produced by vibrating strings are not very loud. Many stringed instruments make use of a sounding board or box, sometimes called a resonator, to amplify the sounds produced. The strings on a piano are attached to a sounding board while for guitar strings a sound box is used. When the string is plucked and begins to vibrate, the sounding board or box begins to vibrate as well. Since the board or box has a greater area in contact with the air, it tends to amplify the sounds.

On a guitar or a violin, the length of the strings are the same, but their mass per length is different. That changes the velocity and so the frequency changes.

Standing waves are produced and the source vibrates in its natural frequencies. The source is in contact with some medium that allows the vibration to propagate.

WIND INSTRUMENTS Wind instruments produce sound from the vibrations ofstanding waves in columns of air inside a pipe or a tube.In a string, the ends are nodes. In air columns the ends can beeither nodes or antinodes.

Open tube

Half Closed Tube

a) For open pipe

The overtones will be multiples of the fundamental

b) For closed pipe

The overtones will be the odd multiples of the fundamental

HARMONICS

INTERFERENCE OF SOUND WAVES: BEATS

If two sources are close in frequency, the sound from them interferes and what we hear is an alternating sound level. The level rise and falls. If the alternating sound is regular, it is called beats.

The beat frequency equals the difference in frequencies between the sources.

This is a way to tune musical instruments. Compare a tuning fork to a note and tune until the beats disappear.

CIConstructive Interference

DIDestructiveInterference

12.1 A saxophone plays a tune in the key of B-flat. The saxophone has a third harmonic frequency of 466.2 Hz when the speed of sound in air is 331 m/s. What is the length of the pipe that makes up the saxophone?

n = 3f3 = 466.2 Hz

v = 331 m/s

f' = f3/n

= 466.2/3 = 233.1 Hz

Saxophone is closed so: L= 1/4 λ

= 0.53 m

1 1

4 4

vL

f

331

4(155.4)

12.2 An organ pipe that is open at both ends has a fundamental frequency of 370.0 Hz when the speed of sound in air is 331 m/s. What is the length of this pipe?

L= 1/2 λ and v = λ f f' = 370 Hzv = 331 m/s

2

vL

f 331

2(370) = 0.447 m

12.3 What is the fundamental frequency of a viola string that is 35.0 cm long when the speed of waves on this string is 346 m/s?

L = 0.35 mv = 346 m/s L= 1/2 λ and λ = 2L

vf

2

v

L 346

2(0.35) = 494.2 Hz

12.4 A pipe that is open at both ends has a fundamental frequency of 125 Hz. If the pipe is 1.32 m long, what is the speed of the waves in the pipe?

f' = 125 HzL = 1.32 m

L= 1/2 λ and λ = 2L

v = λ f =2 L f = 2(1.32)(125) = 330 m/s

12.5 A pipe that is closed on one end has a seventh harmonic frequency of 466.2 Hz. If the pipe is 1.53 m long, what is the speed of the waves in the pipe?

n = 7f7 = 466.2 Hz

L = 1.53 m

L= 7/4 λ and λ = 4/7 L

41(1.53)466.2

7

4

7

Lv f

= 407.6 Hz

DOPPLER EFFECTWhen a source of sound waves and a listener approach one another, the pitch of the sound is increased as compared to the frequency heard if they remain at rest. If the source and the listener recede from one another, the frequency is decreased. This phenomenon is known as the Doppler effect.

DOPPLER EFFECT:The pitch heard by the listener is given by the following equation:

f fv v

v vSo

S

'

Units: Hz

f' is the frequency of the sound heard by the listener (observer), fS is the frequency of the sound emitted by the source,

v is the speed of sound in air, vS is the velocity of the source, and

vo is the velocity of the listener (observer).

Sign Convention: (+) for approaching velocities and (-) for receding velocities.

Light waves also exhibit the Doppler effect. The spectra of stars that are receding from us is shifted toward the longer wavelengths of light. This is known as the red shift.

Measurement of the red shift allows astrophysicists to calculate the speed at which stars are moving away. Since almost all stars and galaxies exhibit a red shift, it is believed that the universe is expanding.

SHOCK WAVES AND THE SONIC BOOMWhen the speed of a source of sound exceeds the speed of sound, the sound waves in front of the source tend to overlap and constructively interfere. The superposition of the waves produce an extremely large amplitude wave called a shock wave.

The shock wave contains a greatdeal of energy. When the shock wave passes a listener, this energy is heard as a sonic boom. The sonic boom is heard only for a fraction of a second; however, it sounds as if an explosion has occurred and can cause damage.

12.6 A train whistle emits sound at a frequency of 400 Hz on a day when the speed is 340 m/s. a. What is the pitch of the sound heard when the train is moving toward a stationary observer at a speed of 20 m/s?

v = 340 m/sfS =400 Hz

vS = 20 m/s' o

sS

v vf f

v v

340 0400

340 20

= 425 Hz

b. What is the pitch heard when the train is moving away from the observer at this speed?

vS = - 20 m/s

' 340 0400

340 20f

= 377.78 Hz

12.7 A stationary source of sound has a frequency of 800 Hz on a day when the speed of sound is 340 m/s. What pitch is heard by a person who is moving from the source at 30 m/s?

v = 340 m/sfS = 800 Hz

vO = - 30 m/s

340 30800

340

' os

S

v vf f

v v

= 729.4 Hz