Sound Waves
What Causes Sound?
VIBRATIONS
Sound Waves
Molecules in the air vibrate about some average position
creating the compressions and rarefactions. We call the
frequency of sound the pitch.
Longitudinal Waves vs. Transverse
– Longitudinal waves follow the same “rules” as the
transverse waves we have dealt with previously.
– However, because cohesive forces between
particle are necessary for transverse wave
propagation, transverse waves only travel on the
surface of fluids.
– Where as, longitudinal waves may propagate
through the “bulk” of a fluid, because they rely on
pressure forces, not cohesive forces. (Pressure
Gun DEMO)
The Fundamentals of
Sound Waves
Sound waves are longitudinal waves

Frequency
– number of oscillations in
pressure per second

Wavelength
– distance between each
successive region of high or
low pressure.
The Speed of Sound

Molecules of the medium collide, allowing
the wave to be transmitted through it.
– The speed of sound depends on elasticity
of the medium.
– The more elastic the medium, the faster
the sound.
– Elasticity – the ability of a solid to return
to its original shape after external forces
have been exerted on it. (16.6 for more)
The Medium

What if there is no medium?
– A vacuum perhaps…

Waves in different media
– In what medium will sound travel
fastest… Steel, wood, or you?
What does the speed of sound depend
upon?
The Medium
Visualizing Sound
Ruben’s Tube
2D Pyro Board
Echo Location and Sonar
Loudness

Loudness - depends on the amplitude
of sound wave
– Again, the amplitude of a wave indicates
its energy. The greater the amplitude, the
greater the energy. (DB Mic. DEMO)
On the graphs to the right
Where is the sound loudest?
16.7 – 16.8


LOUDNESS
The intensity of a sound is proportional to the square
of the amplitude of the sound wave. (E ≈ I ≈ A2)
Loudness is measured in decibels (dB)
VIBRATING
LOUDSPEAKER


1
AMPLITUDE
MICROPHONE
10
100
OSCILLOSCOPE
1000
The decibel scale is logarithmic, increasing by factors
of 10
Sound Intensity (E≈I≈A2)



Sound intensity is the sound power as
it passes through a given area
I = P / Area… (W/m2)
So... I = P / 4Π r2… for a sphere
Sound Intensity (E≈I≈A2)



Sound Intensity is not the same as
Sound Intensity Level!!!
Io = 1 x 10-12 W/m2 (threshold of hearing)
Intensity Level, β, is a comparison of
two sound intensities (Ratio)
β = (10 dB) log10 (I / Io)
Sound Level (dB’s)

β = (10 dB) log10 (I / Io)
If the intensity, I, exceeds the
reference intensity, Io, by a factor of 4,
the intensity level is???
β = (10 dB) log10 (4)
β = 6 dB
Can we measure sound intensity? – YES!
Units of Sound Level Intensity: decibels (dB),
which is a logarithmic scale
An increase in 10 decibels of sound level intensity,
or 10 dB, is perceived to be two times louder (21)
Example: Normal conversation is 60 dB,
and a vacuum cleaner is 80 dB
4x’s
Question: How is the change in sound perceived?
(vacuum cleaner compared to normal conversation? (22)
Typical Sound Intensities
Near total silence A whisper Normal conversation A lawnmower iPod (at full volume) A car horn A rock concert or a jet engine A gunshot or firecracker -
0 dB
15 dB
60 dB
90 dB
100 dB
110 dB
120 dB
140 dB
Rule: Each 10 dB is ten times the sound intensity!
Therefore, the difference between a gunshot and
total silence is 1014 times the INTENSITY!!
NOTE: The Sound LEVEL would be 214 or 16,384 X’s greater!!
Other notable sound intensities
85 dB - Raise your voice so that others may hear
(time for hearing protection!!!)
90 dB for eight hours: Damage to your ears
140 dB sound: Immediate damage to ears
120 dB: The F/A-18 Hornet
Noise Abatement: PA Turnpike
Warrendale Plaza Noise Walls
Noise Abatement Example:
The Automobile Muffler
Muffler Animation
Bose Noise Canceling Headphones
Sound Levels
Loudness is measured in Decibels (dB)
(more on page 487)
– Breathing
– Normal Speech
– Concert
– Pain Threshold
10
60
115
120
dB
dB
dB
dB
Sound and Pitch

Pitch - the frequency of a sound wave
– The human ear is not equally sensitive to
all frequencies (EAR VISUAL & discussion)
Most people cannot hear frequencies below
20Hz or above 16,000Hz (Audible ʄ DEMO)
 Most people are most sensitive to frequencies
between 1,000 and 5,000 Hz
 Battle of the Ages
Musical Scale
 Example “middle C” has a frequency of 262 Hz.

υ =fx
- Where υ is the speed of LIGHT
- (3.0 x 108 m/s)
- f is 102.5 x 106 Hz (102.5 MHz)
 =?

Natural Frequency &
Resonance

Natural frequency (Singing Rod DEMO)
– An object’s own set of frequencies
– Depends primarily on elasticity and shape
vs
Resonance
When the frequency of a forced vibration
matches the an object’s natural
frequency, a dramatic increase in
amplitude occurs (PVC Fisher Burner
Demo)
Tacoma Narrows Bridge

Unfortunately, resonance is not always
a good thing…
Standing Waves on a String
(Transverse fixed at both ends)




For a string with length L, Period T, &
frequency ƒ1… Where T = 1/ ƒ1
And travels there and back, 2L…
The time necessary is t = 2L / v,
where v is the speed of the wave
We find 1/ ƒ1 = 2L /v or …
ƒ1 = v / 2L
for 1st Harmonic
Transverse and Longitudinal
Standing Waves
– Transverse fixed Both ends

ƒn = n v/2L (n = 1, 2, 3, 4…)
Transverse and Longitudinal
Standing Waves
– Longitudinal Open at both ends

ƒn = n v/2L (n = 1, 2, 3, 4…)
Transverse and Longitudinal
Standing Waves
– Longitudinal Open at One end

ƒn = n v/4L (n = 1, 3, 5, 7…)
Noise & Noise Reduction

Noise
– sound of any kind (especially
unintelligible or dissonant sound)

Noise Reduction (SONO) prototype
– LORD Corporation – Aerospace
Engineering
– The use of destructive interference to
eliminate noise
SONO – Noise Cancellation (Prototype)
Doppler Effect

Doppler Shift - Change in sound
frequency due to the relative motion
of either the source or the detector.

example: a passing car
DOPPLER EFFECT


Refers to the change in frequency when there
is relative motion between an observer of
waves and the source of the waves
Doppler with Sound
Diffraction and Sound

Bending of sound around a barrier
Diffraction and Sound
PD = Path Difference
(in terms of λ‘s)
Phase Difference and Path-Length Difference
Δθ = 2Π (ΔL)
λ
Where 2Π represents a full wave cycle or wavelength, & L
is in terms of λ…
Ex:
Δθ = 2Π (ΔL) = 2Π (4λ - 3λ) = 2 Π rads
λ
λ
So… What does that mean… Δθ = 2 Π rads ????
Phase Difference and
Path-Length Difference
Δθ = 2Π (ΔL)
λ
So… What does that mean… Δθ = 2 Π rads ????
When Δθ = 2 Π rads … the waves are shifted by one full λ
So Δθ = 0°… So they are in phase… or constructive
Conditions for Cons. and
Dest. Interferece

ΔL = n λ (where n = 1, 2, 3, etc…)
– Constructive

ΔL = (n + 0.5) λ (where n = 1, 2, 3,
etc…)
– Destructive
Single Slit Diffraction
NOTE:
Node b/c cancellation
takes place
Single Slit (1st Minimum)



D Sinθ = mλ
(where m = 1)
Hence, 1st minimum
Circular Opening (1st Minimum)
D Sinθ = 1.22 m λ
Double Slit Diffraction
Double Slit Diffraction

w Sinθ = mλ…
Constructive

w Sinθ = (m + .5) λ…
Destructive
Sound Refraction
Sonic BOOM


An aircraft traveling through the atmosphere
continuously produces air-pressure waves similar
to the water waves caused by a ship's bow.
When the aircraft
exceeds the speed
of sound, these
pressure waves
combine and form
visible shock
waves 
Sub & Super Sonic
Subsonic - slower than the speed of sound
Supersonic - Faster than the speed of sound

Mach Number =
speed of
object
speed of
sound
Bow waves
V-shaped pattern made by overlapping
crest
Shock Waves


Produced by supersonic aircraft,
three-dimensional cone shaped
Sonic boom – sharp crack heard
when conical shell of compressed air
that sweeps behind a supersonic
aircraft reaches listeners on the
ground below.
The Physics of Music

What is the source of sound, again?
VIBRATIONS

The 3 Types of Musical instruments
All create Vibrations in air
Type
String
 Wind
 Percussion
Membrane

Origin
Plucked String
Mouthpiece or Reed
Stretched
For the Music Folks!
Sound Quality
 Fundamental and Harmonics
 Dissonance and Consonance
 Intervals and Octave
– Beat Notes (DEMO)
– Superposition of waves Demo
Harmonic Content & the
Physics of the Guitar
Concepts of Physics
Chloe & Max Kuffer
Three Ways to
Distinguish Sounds Physically

Intensity
– Interpreted by the human brain as
loudness

Frequency
– Interpreted by the human brain as pitch

Harmonic Content
– Interpreted by the human brain as a
component of the timbre
Human Audible Range
The 12 Tone Scale


For much of “western” music, we limit ourselves to
a choice of only 12 notes, and often only use 8 of
them, to make it less likely that sounds will
combine and be dissonant.
The piano uses a “12 tone evenly tempered
chromatic scale” with middle C at 261.6 Hz
Music vs. Noise



Most pieces of music set up a limited
amount of dissonance on purpose, and
then resolve it to a consonant
conclusion.
The (sometimes unconscious) sense of
relief we feel is part of the experience
of listening to music.
“Noise” contains a great deal of
dissonance and provides no relief!
Timbre: Sound Quality



The characteristics of a sound which allow
the human to distinguish between sounds of
the same pitch and loudness
For example why does a flute playing a “C”
sound differently from a guitar playing the
same note?
There are three contributors to timbre...
– Attack and Decay
– Vibrato
– Harmonic Content (the most important
contributor)
Attack and Decay

Describes how quickly the amplitude of the sound
reaches a maximum and how quickly it dies out
– Ex: a guitar string...quick attack, long gradual decay
– Ex: a cymbal...instant attack, very long, but
initially steep, decay
Attack and Decay


How would you describe the attack and
decay of these sounds?
What musical instruments do you think
they are?
instrument #1
instrument #2
Oboe
Piccolo
Vibrato/Tremolo
The ordinary definition of vibrato is "periodic changes in the pitch of the
tone", and the term tremolo is used to indicate periodic changes in the
amplitude or loudness of the tone. So vibrato could be called FM
(frequency modulation) and tremolo could be called AM (amplitude
modulation) of the tone.
Vibrato is considered to be a desirable
characteristic of the human voice if it is not
excessive.
Guitar Vibrato/Tremolo
Harmonic Content
For sustained tones, the most important
component of timbre is the harmonic
content...the number and relative intensity
of the “harmonics” present in the sound.
 Almost all sounds, except pure tones,
contain many harmonic frequencies...each
frequency is characterized by a sine wave.
 These harmonics consist of a “fundamental”
frequency and a series of overtone
frequencies
 When superpositioned, these harmonics
create a unique “waveform”
Waveform
Harmonic Content
A 300 Hz sound
Harmonic Content
A 500 Hz Sound
Harmonic Content
The blue waveform:
The superposition of a 300 Hz and 500 Hz sound of equal volumes
Harmonic Content
The blue waveform:
The superposition of a 300 Hz and 500 Hz sound of equal volumes
Any complex waveform can be treated as a combination of simple sine waves
EX: Your voice or any musical instrument has a unique waveform.
Harmonic Content for
Trombone
Playing a fundamental
frequency of 155 Hz
Harmonic Content for
Clarinet
Playing a fundamental
frequency of 156 Hz
Harmonic Content on a
Guitar String
Harmonic Content for
Human Voices