Sound
Mark Lesmeister
Dawson High School Physics
This presentation is intended solely for use by Dawson High School Pre-AP
Physics students.
SECTION 1: INTRODUCTION
TO SOUND
Nature of Sound Waves
Sound waves are the result of vibrating
molecules of air, water or other medium.
 Sound waves are longitudinal waves.

Animation courtesy Dan Russell, Kettering University
Nature of Sound Waves
Sound waves are the result of vibrating
molecules of air, water or other medium.
 Sound waves are longitudinal waves.



Motion of the medium is parallel to direction of
travel of the wave.
Sound waves consist of compressions and
rarefactions.
Compression
Is to
Rarefaction
Crest
as
Is to
Trough
High density
as
Is to
Low density
Nature of Sound Waves
Sound waves are the result of vibrating
molecules of air, water or other medium.
 Sound waves are longitudinal waves.
 Sound waves spread out in three
dimensions.

Animation courtesy Dan Russell, Kettering University
Frequency of sound waves

The frequency of an audible sound wave is
related to its pitch.

Sound waves vary greatly in frequency.
Sound
Waves
Infrasonic
Audible
Sounds
Ultrasonic
<20 Hz
>20 Hz
<20,000 Hz
>20,000 Hz
Frequency of sound waves

20 Hz
Wave Sound

880 Hz

80 Hz
Wave Sound

2200 Hz
Wave Sound

160 Hz
Wave Sound

4400 Hz
Wave Sound

220 Hz

8800 Hz
Wave Sound

440 Hz

13200 Hz

22000 Hz
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Wave Sound
Use of Ultrasonic Waves

Ultrasonic waves can be used to produce
“ultrasound” images of objects inside the
body.


These images do not involve harmful X-rays.
The size of the ultrasonic wavelength limits the
size of objects that can be seen.
vf λ
f  10 MHz  107 Hz
v  1500 m/s
  1.5  10-4 m  0.15 mm
Warning:

The next slide shows an image of a 28
weeks gestational age fetus.
4-d Ultrasound Image
Source:
Wikipedia
PART 2: THE MATHEMATICS
OF SOUND
The Speed of Sound

The speed of sound depends on the
medium.
Animation courtesy Dan Russell, Kettering University
The Speed of Sound

The speed of sound depends on the
medium.



The more rigid the medium, the faster sound
travels through it.
The temperature of the medium may affect the
speed of sound.
The speed of sound of some common
materials is given on page 482.



Air: 331 m/s at 0 oC, 346 m/s at 25 oC
Water: 1490 m/s at 25 oC
Metals: Al- 5100 m/s, Cu- 3560 m/s
Mach Numbers
The speed of sound in air is also known as
Mach 1.
 A plane flying at Mach 2 is flying twice the
speed of sound.
 The shuttle flies at a speed of about Mach
25.

The Doppler Effect
The Doppler Effect: Waves from a
Moving Source
Animation courtesy Dan Russell, Kettering University

v=f  so a smaller wavelength means a higher
frequency.
The Doppler Effect:
Waves as seen by a moving observer.
Animation courtesy Dan Russell, Kettering University
The Doppler Effect
The Doppler Effect

Motion of either the source or the observer of a
wave causes the frequency to shift.

If the relative motion results in more wave crests
reaching the observer per second, the frequency
is increased.

If the relative motion results in fewer wave crests
reaching the observer per second, the frequency
is decreased.
Calculating Doppler Effect: Moving
Observer


A moving observer will detect additional
wavefronts per second because of the
motion.
vsound  vobserver
f ' f (
)
vsound
Calculating the Doppler Effect:
Moving Source
 '    d
 '    vsourceT
d
vsource
'   
f
vsound vsound vsource vsound  vsource



f'
f
f
f
f'
f

vsound vsound  vsource
vsound
f ' f (
)
vsound  vsource
Doppler Effect

 vsound  vobserver 

f '  f 
 vsound  vsource 

Use the upper signs when the objects are
moving toward each other, and the
bottom signs when they are moving away.
Sound Intensity

All waves transfer energy.

Power is the rate of energy transfer.

Intensity is the rate of energy transfer through a
unit of area.
P
I
area

In general,

For a spherical wave,
P
I
2
4 r
Courtesy of Dr. Dan Russell,
©2008 by W.H. Freeman and Company
Kettering University
Calculating Intensity

P
intensity 
4 r 2




P = power
r = distance from the source.
Intensity is measured in W/m2.
What is the intensity of sound waves from
an electric guitar at a distance of 5.0 m
when its power output is 0.50 W?

1.6 x 10-3 W/m2
Interpreting Intensity



Intensity and
frequency determine
which sounds are
audible.
The threshold of
hearing has
frequencies around
1000 Hz and
intensities of
1.0 x10-12 W/m2.
The threshold of pain
occurs at about 1.0
W/m2.
1.0 x 10-12 W/m2
1.0 W/m2
Range of Hearing
Diagram from Holt Physics, © Holt, Reinhart and Winston 2002.
Loudness and Decibel level

The intensity of a sound is related to its loudness or
volume.

When intensity increases by a factor of 10, loudness
approximately doubles.


X 10 in intensity means X2 in loudness.
A decibel level relates the intensity of a sound to the
threshold of hearing intensity.


The decibel scale is based on powers of 10.
X 10 in intensity means + 10 dB
Decibel level
dB Level
Increase in
Intensity
Approximate
loudness increase
10 dB
10 X
2X
20
100 X
4X
30
1000 X
8X
Table taken from Holt Physics, © Holt, Reinhart and
Winston 2002.
Decibel Calculations

 I
dB  10 log  
 I0 
I 0  reference level
(for sound, usually th e threshold of hearing)


Example 1: A certain loudspeaker doubles the
intensity of a sound wave. What is the
corresponding dB increase?
Example 2: What is the intensity of a 75 dB
sound wave if the reference level is 10-12 W/m2?
SOUND PHENOMENA
Warm-up: Discovery Lab Activity



Hold the tube
vertically, so that it is
partially submerged in
the water in the cup.
Strike the tuning fork
and place it over the
top of the tube.
Slowly change the
position of the tube,
up and down, and
listen for any changes
in the sound.
Resonance

Many systems have a natural frequency of
vibration; for example

Simple harmonic oscillators





Pendulum
Mass and spring system
Piano strings, other musical instruments.
Resonance occurs when the frequency of a force
applied to a system matches the natural
frequency of vibration of the systems.
A resonance will result in a large amplitude of
vibration.
Standing Waves and Harmonics
When certain systems, such as strings or
air columns, are vibrated, standing waves
are produced.
 Only standing waves of certain
frequencies are possible.


Those frequencies are called harmonics of the
system.
Standing Waves on a String

A stretched string will
produce harmonics
with wavelengths that
will “fit” on the string.

If L is the length of
the string, the allowed
wavelengths are 2L, L,
(2/3)L, (1/2)L, etc.
Graphic from Holt Physics © Holt, Reinhart and Winston 2002.
Harmonic Series of Standing Waves:
Vibrating String

v
fn  n
n  1, 2, 3, ...
2L
speed of waves on the string
frequency  harmonic number 
(2)(length of the string)
Standing Waves in an Air Column

Standing waves can be set up in an air
column.

A closed end of an air column will always
be a node.

An open end of an air column will always
be an antinode of a standing wave.
Harmonic Series of Standing Waves:
Pipe Open at Both Ends

Flutes and similar instruments are modeled as
pipes open at both ends.
Graphic from Holt Physics © Holt, Reinhart and Winston 2002.
Harmonic Series of Standing Waves:
Pipe Open at Both Ends
fn  n
v
n  1, 2, 3, ...
2L
speed of sound in the pipe
frequency  harmonic number 
(2)(length of vibrating air column)
Graphic from Holt Physics © Holt, Reinhart and Winston 2002.
Harmonic Series:
Pipe Closed at One End

Clarinets and brass instruments can be modeled
as pipes closed at one end.
Graphic from Holt Physics © Holt, Reinhart and Winston 2002.
Harmonic Series:
Pipe Closed at One End
v
fn  n
n  1, 3, 5,...
4L
speed of sound in the pipe
frequency  harmonic number 
(4)(length of vibrating air column)
Graphic from Holt Physics © Holt, Reinhart and Winston 2002.
Harmonics and Wind Instruments
Other reed instruments such as
saxophones, oboes and bassoons,
although they are closed at one end,
behave more like a cone than a cylinder.
 The result is that their resonances are
closer to a pipe open at both ends.

Harmonics and Timbre
Sounds with the same frequency can
sound quite different.
 The difference is the result of the presence
of different harmonics at different
intensities.
 The characteristics of a musical note that
result from the different harmonics it
contains are called timbre.
 The fundamental frequency determines
the pitch of the sound.

Sample Timbres
440 Hz tone
 440 Hz and 880 Hz
 First 5 harmonics of 440 Hz, each with ½
intensity of previous one.
 First 5 odd harmonics of 440 Hz, each
with ½ intensity of previous one.
 “Clarinet” playing scale.

Beats

Sound waves of slightly different
frequencies produce beats.

440 Hz and 441 Hz together
Beats are the result of constructive and
destructive interference.
 The frequency of the beats is equal to the
difference in frequency of the two sound
waves.


440 Hz and 442 Hz together.
Some Musical Intervals

Unison- e.g. middle C and middle C


Octave- e.g. middle C and high C



A note with double the frequency.
The first harmonic of this note equals the second harmonic of
the original note.
Fifth- e.g. C and G



A note with the same frequency.
A note with 3/2 the frequency.
The second harmonic of this note equals the 3rd harmonic of the
original note.
Fourth- e.g. C and F


A note with 4/3 the frequency.
The third harmonic of this note equals the fourth harmonic of the
original note.