# Sound

```Sound
Chapter 13
Sound Waves
 Sound waves are areas
of alternating high and
low molecular densities.
 Longitudinal
 Caused by vibrations
 Compression-areas of
high molecular density
 Rarefactions-areas of
low molecular density
Speed of Sound
 The speed of sound depends on the
medium in which it propagates.
 Solids
Liquids
Gases
 Hot
Cold
 (Fast to Slow)
vair  331 0.6T
Human Hearing
 Audible Sounds
 Humans can hear frequencies (known as
pitch) between 20 Hz and 20,000 Hz
 Frequencies higher than we can hear…
 Ultrasonic
 Frequencies lower than we can hear…
 infrasonic
Sound Characteristics
 Pitch-results from differences in frequency
 The higher the frequency, the higher the pitch
 Don’t directly observe wavelength
 Infrasonic and Ultrasonic
 Loudness-results from amplitude
 Logarithmic relationship between intensity and
perceived loudness.
 Increasing intensity by 10 times only results in a
doubling of perceived loudness.
Intensity
Power
Intensity 
Area




Rate at which energy flows
Inverse square relationship
Units of W/m2
We will assume the sound spreads in all
directions equally so the area we are dealing
with is the surface area of a sphere (4πr2).
Intensity and Human
Hearing
 Intensity ranges:
 Threshold of Hearing to Threshold of Pain
 1.0 x 10-12 W/m2 to 1 W/m2
 This is a large range:
 Logarithmic scale compresses this range
 Use Decibel levels
The Decibel Scale
 Hearing damage
starts at 85dB
 For each 10dB step,
the intensity
increases by 10
times and the
perceived loudness
increases by 2 times.
Examples
1.
Calculate the intensity of the sound waves from an
electric guitar’s amplifier at a distance of 5.0 m when its
power output is equal to each of the following values:
a. 0.25 W
b. 0.50 W
c. 2.0 W
2.
If the intensity of a person’s voice is 4.6 x 10-7 W/m2 at a
distance of 2.0 m, how much sound power does that
person generate?
3.
The power output of a tuba is 0.35 W. At what distance
is the sound intensity of the tuba 1.2 x 10-3 W/m2?
The Doppler Effect
 The shift in perceived frequency of a wave due to
relative motion between the source and the observer.
 Observable in both sound (pitch) and light (red and
blue shifts)
 As the sound approaches - higher f
 As sound leaves - lower f
 Occurs as either listener or source is moving
Forced Vibrations and
Natural Frequency
 Forced Vibration – a vibration that occurs
when a periodic force causes an object to
vibrate at a particular frequency
 Singing
 Natural Frequency – the frequency an
object will vibrate at when given a one
time force
 Depends on shape and material of object
Resonance
 The amplified wave
that occurs when a
forced vibration on an
object matches the
natural frequency of
the object.
 Makes the wave
progressively larger.
 Swing set example
Music
 Different notes have different
mathematical relationships
between their frequencies.
 Specific frequency
combinations are considered
pleasant (harmony) and others
unpleasant (dissonance).




2:1 = Octave (C to the next C)
5:4 = Major Third (C to E)
4:3 = Perfect Forth (C to F)
3:2 = Perfect Fifth (C to G)
Instruments
 The sound produced by the vibration of a
piece of the instrument (string, reed, lips)
is amplified and shaped through
resonance by the rest of the instrument.
 Standing waves are produced within the
instrument at certain frequencies
depending on either the properties of the
string or the shape and size of the
instrument.
Strings
 Physically, wavelength is
restricted to certain values.
 To change those values, the
length of the string needs to
be changed (different keys
on a piano, different finger
placements on a guitar)
 The longest wavelength on
the string is the sound you
hear as the note being
played and is called the
fundamental or first
harmonic.
Wavelengths
L  1 2 1
1  2 L
 The higher frequency vibrations are played
simultaneously and are called overtones. Therefore,
the next longest wavelength will be the second
harmonic or first overtone.
L  2
L  3 2 3
L  24
3  2 3 L
4  1 2 L
Frequencies
2L
n 
n
 Since all of the waves are on the same medium and
travel at the same speed, there will be a pattern to the
frequency as well as the wavelength.
v  n f n
v
n
 fn
v
nv

 fn
2L
2L
n
v
f1 
2L
f n  nf1
Closed Pipe
 Node on one end, antinode on the other.
 Diagrams help with determining wavelength
pattern.
Wavelengths and
Frequencies
4L
n 
n


Where n=1, 3, 5…
Closed pipes have
only odd harmonics
v  n f n
1  4 L  1
L  3 4 2  4 3 L  2
L  5 4 3  4 5 L  3
L
1
4
fn 
v
n
v
nv
fn 

4L
4L
n
f n  nf1
Open Pipes
 The same as the closed pipe, however there is
an anti-node at each end for molecular
movement and a node at each end for
pressure variance.
Wavelengths and
Frequencies
2L
n 
n
v  n f n
L
1
2
1  2 L  1
L  2
L  3 2 3  2 3 L  3
fn 
v
n
v
nv
fn 

2L
2L
n
f n  nf1
Beats
 Beats are a result of two waves
with close, but not identical
frequencies.
 A pattern of constructive and
destructive interference forms
creating a warbling sound.
 Useful for tuning instruments.
 Beat frequency is equal to the
difference between the two
component frequencies.
Timbre
 The unique combination of
intensities of fundamental
and overtone frequencies
that makes instruments
sound different when playing
the same note.
Trumpet
Flute
Cello
Examples
1.
What is the fundamental frequency of a 0.2 m long organ pipe that is
closed at one end, when the speed of sound in the pipe is 352 m/s?
2.
A flute is an open pipe. The length is the flute is approximately 66.0
cm. What are the first three harmonics of a flute when all keys are
closed, making the length of air equal to the length of the flute? Use
340 m/s for the speed of sound.
3.
What is the fundamental frequency of a guitar string when the speed
of waves on the string is 115 m/s and the effective string lengths are
as follows:
a.
b.
c.
4.
70.0 cm
50.0 cm
40.0 cm
A violin string that is 50.0 cm in length has a fundamental frequency
of 440 Hz. What is the speed of the waves on this string?
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