Sound

1
Chapter 12

• Sound

2
Sound, A special kind of longitudinal wave
Consider a vibrating guitar string
3
Sound

• Producing a Sound Wave
• Sound waves are longitudinal waves traveling
  through a medium
• A tuning fork can be used as an example of
  producing a sound wave

4
Using a Tuning Fork to Produce a Sound Wave

• A tuning fork will produce a pure musical note
• As the tines vibrate, they disturb the air near
  them
• As the tine swings to the right, it forces the
  air molecules near it closer together
• This produces a high density area in the air
• This is an area of compression

5
Using a Tuning Fork, cont.

• As the tine moves toward the left, the air
  molecules to the right of the tine spread out
• This produces an area of low density
• This area is called a rarefaction

6
Using a Tuning Fork, final

• As the tuning fork continues to vibrate, a
  succession of compressions and rarefactions
  spread out from the fork
• A sinusoidal curve can be used to represent the
  longitudinal wave
• Crests correspond to compressions and troughs to
  rarefactions

7
What IS Sound?

• Sound is really tiny fluctuations of air pressure
• units of pressure N/m2 or psi (lbs/square-inch)
• Carried through air at 343 m/s (770 m.p.h) as
  compressions and rarefactions in air pressure

wavelength
compressed gas
rarefied gas
8
Properties of Waves
? or T
pressure
horizontal axis could be space representing
snapshot in time time representing sequence at
a par- ticular point in space

• Wavelength (?) is measured from crest-to-crest
• or trough-to-trough, or upswing to upswing, etc.
• For traveling waves (sound, light, water), there
  is a speed (c)
• Frequency (f) refers to how many cycles pass by
  per second
• measured in Hertz, or Hz cycles per second
• associated with this is period T 1/f
• These three are closely related
• ?f v

9
Characteristics of Sound Waves

• Pitch refers to whether the sound is a high or
  low note (pitch -gt frequency)
• Audible waves
• Lay within the normal range of hearing of the
  human ear
• Normally between 20 Hz to 20,000 Hz
• Infrasonic waves
• Frequencies are below the audible range
• Earthquakes are an example
• Ultrasonic waves
• Frequencies are above the audible range
• Dog whistles are an example

10
Longitudinal vs. Transverse Waves

• Sound is a longitudinal wave, meaning that the
  motion of particles is along the direction of
  propagation
• Transverse waveswater waves, lighthave things
  moving perpendicular to the direction of
  propagation

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Why is Sound Longitudinal?

• Waves in air cant really be transverse, because
  the atoms/molecules are not bound to each other
• cant pull a (momentarily) neighboring molecule
  sideways
• only if a rubber band connected the molecules
  would this work
• fancy way of saying this gases cant support
  shear loads
• Air molecules can really only bump into one
  another
• Imagine people in a crowded train station with
  hands in pockets
• pushing into crowd would send a wave of
  compression into the crowd in the direction of
  push (longitudinal)
• jerking people back and forth (sideways, over
  several meters) would not propagate into the
  crowd
• but if everyone held hands (bonds), this
  transverse motion would propagate into crowd

12
Speed of Sound

• Sound speed in air is related to the frantic
  motions of molecules as they jostle and collide
• since air has a lot of empty space, the
  communication that a wave is coming through has
  to be carried by the motion of particles
• for air, this motion is about 500 m/s, but only
  about 350 m/s directed in any particular
  direction
• Solids have faster sound speeds because atoms are
  hooked up by springs (bonds)
• dont have to rely on atoms to traverse gap
• spring compression can (and does) travel faster
  than actual atom motion

13
Example Sound Speeds
Medium sound speed (m/s)
air (0?C) 331
air (20?C) 343
water 1497
gold 3240
brick 3650
wood 38004600
glass 5100
steel 5790
aluminum 6420
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The Speed of Sound

• Speed of Sound in a Liquid
• In a liquid, the speed depends on the liquids
  compressibility and inertia
• B is the Bulk Modulus of the liquid
• ? is the density of the liquid
• Compares with the equation for a transverse wave
  on a string

15
Speed of Sound in a Solid Rod

• The speed depends on the rods compressibility
  and inertial properties
• Y is the Youngs Modulus of the material
• ? is the density of the material

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Speed of Sound, General

• The speed of sound is higher in solids than in
  gases
• The molecules in a solid interact more strongly
• The speed is slower in liquids than in solids
• Liquids are more compressible

Medium Speed (m/s)
Air 343
Helium 972
Water 1500
Steel (solid) 5600
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Speed of Sound in Air

• 331 m/s is the speed of sound at 0 C
• T is the absolute temperature

18
Speed of Sound

• Mach Number Object speed/ Speed of Sound

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Speed of Sound

• Example
• The speed of sound in a column of air is measured
  to be 356 m/s. What is the temperature of the air?

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Energy and Intensity of Sound Waves

• Intensity of Sound Waves
• The average intensity of a wave is the rate at
  which the energy flows through a unit area, A,
  oriented perpendicular to the direction of travel
  of the wave
• The rate of energy transfer is the power
• Units are W/m2

21
Various Intensities of Sound

• Threshold of hearing
• Faintest sound most humans can hear
• About 1 x 10-12 W/m2
• Threshold of pain
• Loudest sound most humans can tolerate
• About 1 W/m2
• The ear is a very sensitive detector of sound
  waves
• It can detect pressure fluctuations as small as
  about 3 parts in 1010

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Intensity Level of Sound Waves

• The sensation of loudness is logarithmic in the
  human hear
• ß is the intensity level or the decibel level of
  the sound
• Io is the threshold of hearing

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Various Intensity Levels

• Threshold of hearing is 0 dB
• Threshold of pain is 120 dB
• Jet airplanes are about 150 dB
• Table 14.2 lists intensity
• levels of various sounds
• Multiplying a given intensity by 10 adds 10 dB to
  the intensity level

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Intensity of sounds

• Some examples (1 pascal ? 10-5 atm)

Sound Intensity Pressure Intensity amplitud
e (Pa) (W/m2) level (dB) Hearing threshold 3 ?
10-5 10-12 0 Classroom 0.01 10-7
50 City street 0.3 10-4 80 Car without
muffler 3 10-2 100 Indoor concert 30 1 120 Jet
engine at 30 m. 100 10 130
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Energy/Intensity Waves

• Example
• A family ice show is held at an enclosed area.
  The skaters perform to music playing at a level
  of 80.0 dB. The intensity level of music playing
  is too loud for your baby brother who yells at
  75.0 dB. (a) What total sound intensity is
  produced? (b) What is the combined sound level?

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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

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Doppler Effect, cont.

• Although the Doppler Effect is commonly
  experienced with sound waves, it is a phenomena
  common to all waves
• Assumptions
• The air is stationary
• All speed measurements are made relative to the
  stationary medium

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Doppler Effect, Case 1 (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

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Doppler Effect, Case 1(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

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Doppler Effect, Case 1 Equation

• When moving toward the stationary source, the
  observed frequency is
• When moving away from the stationary source,
  substitute vo for vo in the above equation

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Doppler Effect, Case 2 (Source in Motion)

• As the source moves toward the observer (A), the
  wavelength appears shorter and the frequency
  increases
• As the source moves away from the observer (B),
  the wavelength appears longer and the frequency
  appears to be lower

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Doppler Effect, Source Moving Equation

• Use the vs when the source is moving toward the
  observer and vs when the source is moving away
  from the observer

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Doppler Effect, General Case

• Both the source and the observer could be moving
• Use positive values of vo and vs if the motion is
  toward
• Frequency appears higher
• Use negative values of vo and vs if the motion is
  away
• Frequency appears lower

34
Doppler Effect

• Example
• As a truck travelling at 96 km/hr approaches and
  passes a person standing along the highway, the
  driver sounds the horn. If the horn has a
  frequency of 400 Hz, what are the frequencies of
  the sound waves heard by the person
• (a) as the truck approaches?
• (b) after it has passed?