Chapter 12

Sound

The Origin of Sound Sound is a longitudinal, mechanical

wave. You can hear sound with a frequency

of 20 – 20,000 Hz. Under 20 hz is infrasonic, and above 20,000 hz is ultrasonic.

We talk about the frequency of sound when it is produced, and the pitch of sound when we hear it.

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The Speed of Sound

The speed of sound depends upon the media in which it travels.

The speed of sound in air is 331 m/s at 0° Centigrade.

V = 331 + (0.6 m/s/°C)T The speed of sound increases by 0.6

m/s for every 1°C increase in temperature in air.

Loudness When a sound is produced it has a certain

intensity. This is defined as:I = Power/Area

Area of the surface of a sphere 4πr2 Or intensity is measured as the ratio of

power divided by the area when the sound is produced.

Loudness is a sensation when we hear a sound. Different people react differently to the same intensity. In other words the same level of sound has a different “loudness” to different people.

Intensity of Sound: Decibels Intensity of sound, (I), is measured in W/m2.

However we often measure the loudness of a sound using a scale of relative intensity, known as the decibel (dB).

Decibels are a logarithmic scale which compares the intensity of a sound to the intensity of sound at the Threshold of Hearing, approximately 10-12 W/m2.

Hence the equation for calculating relative intensity is:

0

log10)(I

IdBin

Sample Problem

What is the relative intensity, in dB, of a sound which has an intensity of 5 x 10-10 W/m2?

Solution

0

log10)(I

IdBin

dBmW

mWxdBin 98.26

/10

/105log10)(

212

210

Forced Vibration and Natural Frequency

When a vibrating object is placed in contact with another object, the second object will also begin to vibrate. This is known as a force vibration.

An object’s natural frequency is one at which it takes a minimum energy to cause it to vibrate.

All object have a natural frequency at which they vibrate easily and if that frequency is within the range of human hearing – the object makes a sound.

Law of Pipes

For an Open Pipe (open at both ends) λ ≈ 2l or λ=2(l+0.8d)

For a Closed Pipe (open at one end) λ ≈ 4l or λ=4(l+0.4d)

In an open pipe all harmonics are present and in a closed pipe only the odd harmonics are present.

Sample Problem

If a pipe is 2 meters long at 0° C: What is its fundamental frequency and

first two harmonics if it is: Open closed

Solution Open pipe:

λ≈2l = 2(2 m) = 4 metersf = V/λ = 330/4 = 82.5 Hz

2nd Harmonic = 2(82.5) = 165 Hz3rd Harmonic = 3(82.5) = 247.5 Hz

Closed Pipeλ≈4l = 4(2 m) = 8 metersf = V/λ = 330/8 = 41.25 Hz

3rd Harmonic = 3(41.25) = 123.75 Hz5th Harmonic = 5(41.25) = 206.25 Hz

Law of Strings There are four

laws which govern the frequency of a string: Length:

Diameter:

Tension:

Density:

l

l

f

f '

'

d

d

f

f '

'

'' F

F

f

f

D

D

f

f '

'

Sample Problem

A violin string has a frequency of 340 Hz when it is 1 meter long. What is its frequency when it is shortened to ½ meter?

When a guitar string is under a tension of 200 newtons it plays a frequency of 330 hz, what will it play if it is tightened to 450 newtons?

Solution

hzffl

l

f

f680

1

5.340'

'

hzffF

F

f

f495

450

200

'

330

''

Interference

When two waves pass through each other they are said to form an interference pattern.

There are two types of interference pattern: Constructive interference

Waves reinforce each other Destructive interference

Waves cancel each other

Standing Waves

When a wave and its reflection reinforce each other they form a standing wave. In a standing wave the parts which don’t

move are called nodes and the parts which move are called anti-nodes.

Nodes are a results of destructive interference and anti-nodes come from constructive interference.

Beats The beat frequency is an interference

pattern which occurs when two frequencies are played at the same time.

The interference pattern has both constructive and destructive parts to it. The constructive parts cause a higher amplitude which is distinguishable from the frequencies being played. Hence a “beat pattern”

The number of beats/second is determined by taking the difference between the two frequencies being played.

Sample problem

If two tuning forks are struck, f1 = 340 hz and f2 = 364 hz, what beat frequency will be heard?

Solutionfb = f2 – f1=364 hz – 340 hz = 24 hz

or24 beats/second

The Doppler Effect When a person listening to a sound is

moving and/or the source of the sound is moving you get the Doppler effect.

When they are getting closer together the sound that is heard is of a higher frequency than the original.

When they are moving apart, the sound that is heard is of a lower frequency than the original.

Doppler Effect: Moving Source- Stationary Listener

Source Approaching – Listener in Front

Source Moving Away – Listener Behind (Lb)

sslf vv

vff

sslb vv

vff

V = speed of sound Vs = speed of source

Sample Problem

A train has a whistle with a frequency of 330 Hz. If a listener on a platform hears the whistle as a train approaches the station at 40 m/s, what frequency does the listener hear?

The temperature is 20 °C.

Solution

hzsmsm

smhz

vv

vff

sslf 5.373)

/40/343

/343(330

Speed of sound = 331 + (20 °C)(0.6 m/s/°C)

Doppler Effect: Moving Listener- Stationary Source

Listener Approaching – Listener Closing

Listener Moving Away – Listener Opening

V = speed of sound Vlc or Vlo = speed of listener

v

vvff lcslc

v

vvff loslo

Sample Problem

A man is driving in his car, approaching a stationary siren with a frequency of 500 Hz. If he is traveling at 25 m/s, what frequency does he hear?

Solution

hzsm

smsmhz

v

vvff lcslc 7.537)

/331

/25/331(500

Speed of sound = 331 m/s. Assume 0° C if not told otherwise.

Bow and Shock Waves

When a source moves as fast or faster than a wave in a media it creates a bow wave. If this is in air then the shock wave is three dimensional and is called a sonic boom.

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