FOUNDATION PHYSICS I

PHY 094
CHAPTER 14: Sound

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Units of Chapter
 13.7 Waves
 13.8 Frequency, amplitude and wavelength
 13.9 Speed of waves on strings
 14.3 Speed of Sound
 14.4 Energy and Intensity of Sound Waves
 14.6 The Doppler Effect
 14.7 Interference of Sound Waves
 14.8 Standing Waves
 14.10 Standing Waves in Air Columns
 14.11 Beats
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 Learning Outcome
At the end of this session, students should be able to:
• To understand the properties of longitudinal waves and
progressive waves.
• To explain the principle of superposition
• To derive and interpret the standing wave equation
• To distinguish between progressive waves and standing
waves.

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 13.7: Waves

A disturbance that propagates from one place to another is

referred to as a wave.

Transverse wave

Types of
Waves
Longitudinal wave

Section 13.7
 Particle Motion:
a) Transverse Wave:
Displacement of the medium is perpendicular to the
direction of motion of the wave

b) Longitudinal Wave:
Displacement of the medium is parallel to the direction of
motion of the wave
13.8: Frequency, Amplitude and Wavelength

Equilibrium
position
Wave crest

Wave trough

1. Amplitude, A
2. Wavelength, λ
3. Period, T
4. Frequency, f
5. Velocity, v
 Periodic Waves

In the drawing, one cycle is shaded in color.

The amplitude A is the maximum excursion of a particle of the medium from

the particles undisturbed position.

The wavelength is the horizontal length of one cycle of the wave.

The period is the time required for one complete cycle. 1

f 
The frequency is related to the period and has units of Hz, or s-1. T
Speed of a wave:
Example 1 : The Wavelengths of Radio Waves

AM and FM radio waves are transverse waves consisting of electric

and magnetic field disturbances traveling at a speed of 3.00x108m/s.
A station broadcasts AM radio waves whose frequency is
1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz.
Find the distance between
adjacent crests in each wave.

 v
v  f 
T f
Solution :
AM

FM
Example 2

Answer:
a) 17.2 m
b) 1.72 cm 11

Section 13.8
Solution :

12

Section 13.8
Example 3 :

A travelling wave of wavelength 0.6m moves at a speed of

3.0 m/s. What is the period of this wave ?
Now you know  = 0.6 m, v = 3.0 m/s
Can you find the frequency of this wave……

Then the period of this wave is ???

 13.9: Speed of waves on strings

The speed of a wave is determined by the properties of

the material through which it propagates.

For a string, the wave speed is determined by:

1. the tension in the string, and
2. the mass of the string.
As the tension in the string increases, the speed of waves
on the string increases as well.
The Speed of a Wave on a String
The speed at which the wave moves to the right depends on
how quickly one particle of the string is accelerated upward in
response to the net pulling force.

tension
F F
v 
m L  linear density
(mass per unit length)

As we can see, the speed increases when the force increases,

and decreases when the mass increases.
 Waves on a String

When a wave reaches the end

of a string, it will be reflected. If
the end is fixed, the reflected
wave will be inverted:

If the end of the string is

free to move transversely,
the wave will be reflected
without inversion.
 14.3: Speed of sound

• Sound created by a vibrating object only

• Sound can be created or transmitted only in a medium ( solid,
liquid or gas)
• Sound cannot exist in vacuum
 Sound Waves
Sound waves are longitudinal waves, similar to the waves
on a Slinky:

Here, the wave is a series of compressions and stretches.

The distance between adjacent condensations is equal
to the wavelength of the sound wave.
 Characteristics of Sound
Sound can travel through any kind of matter, but not through a
vacuum.

The speed of sound is different in

different materials; in general, it
is slowest in gases, faster in
liquids, and fastest in solids.
The speed depends somewhat
on temperature, especially for
gases.
 Sound Waves

Sound waves can have any frequency; the human ear can hear
sounds between about 20 Hz and 20,000 Hz.
Sounds with frequencies greater than 20,000 Hz are called
ultrasonic; sounds with frequencies less than 20 Hz are called
infrasonic.
Ultrasonic waves are familiar from medical applications;
elephants and whales communicate, in part, by infrasonic
waves.
 14.4‐14.5 : Energy and intensity of sound waves

The intensity of a sound is the amount of energy that passes

through a given area in a given time.

Expressed in terms of power,

Example 4 : Sound Intensities

12x10-5W of sound power passed through the surfaces labeled 1

and 2. The areas of these surfaces are 4.0m2 and 12m2.
Determine the sound intensity
at each surface.
Solution :

The sound intensity is less at the more distant surface for the same sound power
passes through both surfaces with different area.
 14-5 Sound Intensity
Sound intensity from a point source will decrease as the
square of the distance.

Area of a sphere

Bats can use this decrease in sound intensity to

locate small objects in the dark.
 14-5 Sound Intensity
The decibel (dB) is a measurement unit used when comparing two sound
intensities.

Because of the way in which the human hearing mechanism responds to

intensity, it is appropriate to use a logarithmic scale called the intensity
level, β:

Here, I0 is the faintest sound that can be heard:

Threshold of hearing

Note that log(1)=0, so when the intensity of the sound is equal to Io, the
intensity level is zero.
 14-5 Sound Intensity

The quantity β is called

decibel.
The intensity of a sound
doubles with each increase in
intensity level of 10 dB.
Example 5

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Section 14.4
Example 6

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Section 14.4
 30

Section 14.4
 14.6: The Doppler Effect

A Doppler effect is experienced whenever there is relative

motion between a source of waves and an observer.

 When the source and the observer are moving toward

each other, the observer hears a higher frequency
 When the source and the observer are moving away
from each other, the observer hears a lower frequency
 14-6 The Doppler Effect
1) Doppler Effect for Moving Observer

 v  vo 
fo  fs  
 v 
SI unit: 1/s = s-1 = Hz
vo = observer speed
v = wave speed

 Substitute (+ v0) for v0 in the equation when the

observer moves toward the source.
 Substitute (– v0) for v0 in the equation when the
observer moves away from the source.
 14-6 The Doppler Effect
Case 1: (Moving Observer)
Observer Toward Source
 An observer is moving toward a stationary source
 Due to his movement, the observer detects an additional
number of wave fronts
 The frequency heard is increased
 When moving toward the stationary source, the observed
frequency is

Observer Toward

 v   vo  
fo  f s  
 v 
Case 1: (Moving Observer)

Observer Away from Source

 An observer is moving away from a stationary source
 The observer detects fewer wave fronts per second
 The frequency appears lower
 When moving away the stationary source, the observed
frequency is

Observer Away

 v   vo  
fo  fs  
 v 
2) Doppler Effect for Moving Source

 v 
fo  f s  
 v  vs 
SI unit: 1/s = s-1 = Hz
vs = source speed
v = wave speed
 Substitute (+ vs) for vs in the equation when the source
moves toward from the observer.
 Substitute (– vs) for vs in the equation when the source
moves away from the observer.
 14-6 The Doppler Effect
Case 2: (Moving Source)

Source Toward Observer

 As the source moves toward the observer (A), the
wavelength appears shorter and the frequency increases
 When source is moving toward the observer, the observed
frequency is

Source Toward

 v 
f o  f s  
 v   v s  
Case 2: (Moving Source)
Source Away from Observer
 As the source moves away from the observer (B), the
wavelength appears longer and the frequency appears to
be lower
 When source is moving away from the observer, the
observed frequency is

Source Away

 v 
f o  f s  
 v   v s  
Combining results gives us the case where both observer and
source are moving:

Doppler Effect for Moving Source and Observer

 v   vo  
f o  f s  
 v   v s  
 SI unit: 1/s = s-1 = Hz
 The Doppler Effect does not depend on distance
 As you get closer, the intensity will increase
 The apparent frequency will not change
 Example 14-5
An ambulance travels down a highway at a speed of 75.0
mi/h, its siren emitting sound at a frequency of 4.00 × 102
Hz. What frequency is heard by a passenger in a car
travelling at 55.0 mi/h in the opposite direction as the car
and ambulance

(a) approach each other and

(b) pass and move away from each other? Take the speed
of sound in air to be v = 345 m/s.
 Solution
a) approach each other

b) pass and move away from each other

 Answer:
f’ = 454 Hz
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f’= 426 Hz
Section 14.6
Exercise

15 m/s

42

Section 14.6
Exercise

70.5 m/s

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Section 14.6
 14.7: Interference of sound waves
Waves of small amplitude traveling through the same
medium combine, or superpose, by simple addition.
 14‐7 Superposition and Interference
If two pulses combine to give a larger pulse, this is
constructive interference (left). If they combine to give a
smaller pulse, this is destructive interference (right).
• Constructive interference occurs when numbers of wavelength
from the two sources differs by
0, 1, 2, 3…..

• Destructive interference occurs when numbers of wavelength

from the two sources differs by
½ , 3/2 , 5/2….

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Section 14.7
 47

Section 14.7
 48

Section 14.7
14.8: Standing waves

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Section 14.8
 14‐8 Standing Waves
The fundamental, or lowest, frequency on a fixed string has a
wavelength twice the length of the string. Higher frequencies
are called harmonics.
 Transverse Standing Waves
Transverse standing wave patterns.

Example of transverse standing wave – guitar string

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Section 14.8
Exercise

77 Hz

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Taken from James S.Walker , 4th edition

Section 14.8
 14.10: Standing waves in air columns

Standing waves can also be

excited in columns of air, such
as soda bottles, woodwind
instruments, or organ pipes.
As indicated in the drawing,
one end is a node (N), and the
other is an antinode (A).

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Section 14.10
 Longitudinal Standing Waves

Tube open at both ends

(Antinode to antinode)

L = n(1/2)n
 v 
f n  n  n  1, 2, 3, 4, 
 2L 
 Longitudinal Standing Waves

Tube open at one end

(Node to antinode)
 v 
L = n(1/4)n f n  n  n  1, 3, 5, 
 4L 
 v v
fn  n  nf 1 n  1, 2, 3,... fn  n  nf1 n  1, 3, 5,...
2L 4L
 58

Section 14.10
 59

Section 14.10
Exercise 1

a) 93.5 Hz b) 31.2 Hz
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Section 14.10
Exercise 2

a) 101 Hz b) 1.7 m
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Section 14.10
 Summary of Chapter 14
 Intensity level, measured in decibels:
 Doppler effect: change in frequency due to relative
motion of sound source and receiver
 General case (both source and receiver moving):

 When two or more waves occupy the same location at

the same time, their displacements add at each point.
 If they add to give a larger amplitude, interference is
constructive.
 Summary of Chapter 14

 If they add to give a smaller amplitude, interference is

destructive.
 An interference pattern consists of constructive and
destructive interference areas.
 Two sources are in phase if their crests are emitted at the
same time.
 Two sources are out of phase if the crest of one is emitted
at the same time as the trough of the other.
 Standing waves on a string:
 Summary of Chapter 14
 Standing waves in a half-closed column of air:

 Standing waves in a fully open column of air:

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