Sound

1
Chapter 26

• Sound

2
The Origin of Sound

• All sounds are produced by the vibrations of
  material objects
• Usually the small vibration stimulates vibration
  of a larger object (the sounding board of an
  instrument, air in the throat and mouth of
  someone talking
• This vibrating material sends a disturbance
  through the surrounding air, that then propagates
  through surroundings in form of longitudinal
  waves
• Usually frequency of original vibration
  frequency of sound waves pitch
• High pitch high frequency (a piccolo), whereas
  low pitch means low frequency (fog horn)
• Human ear can hear between 20 20 000 Hz.
• Infrasonic below 20 Hz
• Ultrasonic above 20 000 Hz

3
Sound in Air

• Longitudinal wave air molecules vibrate to and
  fro along direction of wave
• If you quickly push open the door, the door
  pushes the air molecules next to it away form
  their initial positions and into their neighbor
  particles and the curtain flaps out the window
• Compressed air has moved from the door to the
  window
• This disturbance is called compression
• If you quickly close the door, the door pushes
  the air molecules out of the room and leaves a
  low pressure area (rarefied) and the other air
  molecules move into the rarefied region
• When the low pressured region gets to the
  curtain, the curtain flaps inward (toward the low
  pressure region)
• This disturbance is called rarefraction
• Note again medium (air molecules) are not
  transported across the room rather the
  disturbance, and energy are.
• Swing door open and shut periodically get
  periodic compression-rarefaction wave across the
  room.
• Note compression and rarefaction travel in the
  same direction

4
Sound in Air

• Tuning fork is exactly this action on a
  smaller, faster scale
• prong vibrating is like the door opening and
  shutting.
• Radio loudspeaker cone that vibrates in synch
  with electric signal, causing neighboring air
  molecules to vibrate eventually sound wave
  filling the room

5
Media That Transmit Sound

• Doesnt have to be air just has to have an
  elastic property
• Elastic-- be able to change shape in response to
  an applied force and then resume its original
  shape once force is removed.
• Remember steel is elastic putty is not
• Sound generally travels fastest in solids, then
  in liquids, and slowest in gases
• 15x as fast in steel than air
• 4x as fast in water than air
• Generally less dissipation (fading away) in
  solids and liquids than in air,
• Can hear a distant train coming more clearly if
  put ear against the rail
• Motors of boats or fingernails clicking - sound
  much louder to someone under water, than to
  someone above.
• Liquids and crystalline solids are much better
  conductors of sound.
• Sound needs a medium wont travel in a vacuum
  since nothing to compress and expand

6
Speed of Sound

• TRUE OR FALSE The speed of sound is the same in
  all media.
• False. The speed of sound depends on the medium,
  its temperature, and its elasticity
• Which is fastersound or light?
• Lightyou see lightning much faster than you hear
  thunder (unless you are at the source)

7
Speed of Sound

• The speed of sound in dry air at 0ºC is about 330
  m/s.
• Water vapor in the air increases the speed of
  sound
• For each degree increase in temperature the speed
  of sound increases by 0.60 m/s.
• Speed of sound also depends on elasticity
• Atoms are closer together and transmit energy
  quickly with little loss

8
Speed of Sound

• What is the speed of sound at 50ºC?
• Approximately how far away is a storm if you note
  a 5 second delay between a lightning flash and
  the sound of thunder?

9
Loudness

• Sound intensity is proportional to the square of
  the amplitude of a sound wave
• Loudness is a physiological sensation in the
  brain
• Loudness is subjective, but is related to sound
  intensity
• Sound intensity is measured in decibels (dB)
• Loudness varies as the logarithm (base 10) of
  intensity
• A 20 dB sound is 10 times as intense as a 10 dB
  sound (not twice as dense)

10
Force Vibrations

• When force an object to vibrate at a certain
  frequency
• Tuning fork hit it in air and the sound is quite
  faint.
• But if you hit it, and then hold on table, the
  sound is louder, because table is forced to
  vibrate too with its larger surface area, more
  air molecules made to vibrate
• The table top becomes a sounding board
• Music boxes and stringed instruments use sounding
  boards and force vibrations

11
Natural Frequency

• Drop different objects on the floor and you hear
  different sounds
• Natural Frequency--characteristic frequency (or
  frequencies) that an object tends to vibrate at,
  if disturbed.
• But not forced by an external vibrating object
• At natural frequency minimum energy is required
  to produce forced vibrations
• Determined by elastic properties and shape of the
  object
• So only elastic objects have natural frequencies
  putty does not
• Not just a property of sound waves
• Pendulum has a natural frequency determined by
  its length if released, will oscillate with
  that frequency

12
Resonance

• Resonance occurs when frequency of forced
  vibration objects natural frequency
• A dramatic increase in amplitude (loudness)
  results
• Pumping legs when on a swing pump in rhythm with
  the swings natural frequency, and you go higher.
  
• Or, get someone to push you at in rhythm with
  swing - i.e. in resonance .
• Note that if you are pushed really forcefully but
  not in resonance, you dont go higher timing is
  more important than force.
• DEMO two separated same-frequency tuning forks.
  Striking one sets the other into vibration! Often
  called sympathetic vibration.

Heres whats happening to the second fork
13
Resonance

• Note that if the forks did not have matched
  frequencies, the timing of the pushes with the
  natural inclination of the second fork will be
  off wont get increased amplitude.
• Same principle when tune your radio!
• You are adjusting the natural frequency of the
  electronics to match an incoming signal
• Very important in musical instrument design.
• Resonance is not restricted to wave motion
• This is why soldiers break step when crossing
  bridges in 1831, British troops inadvertently
  marched in resonance (in rhythm) with the natural
  frequency of a footbridge, breaking it.
• Also why, in 1940, this bridge in Washington was
  destroyed by a resonance with the wind!

14
Interference

• Sound waves can interfere (like any waves)
• Longitudinal waves can interfere constructively
  and destructively

Crest of longitudinal wave is area of
compression Trough of a longitudinal wave is
area of rarefaction
15
Interference

• Interference affects the loudness of sounds
• Consider two speakers emitting same frequency
  sound
• If sit equidistant from each, then speakers add,
  sound is louder (picture a) constructive
  interference.
• If move a bit to one side, then compression of
  one meets rarefactions of other, sound is gone
  (picture b) destructive interference.

• For certain path-length difference, you get
  constructive or destructive interference. It
  depends on the frequency.
• Usually speakers emit variety of frequencies
  only some destructively interfere for a given
  path-length difference. So usually not a problem,
  esp. when reflecting surfaces around.

16
Interference

• Another example of sound interference Consider
  driving two speakers with same signal, but
  switching the and inputs on one of them.
• This makes them out of phase.
• Get almost no sound when brought face-to-face -
  destructive interference as compression regions
  from one overlap with rarefaction from other.
• Anti-noise technology need in jackhammers.
• Electronic microchips produce mirror-image wave
  patterns of the sound. This is fed to headphones,
  so to cancel out the loud noise for the operator,
  while enabling him to still hear co-workers
  voices!
• These devices cancel about 95 of the original
  noise.

17
Beats

• Beats are a periodic variation in loudness
  (amplitude)
• Throbbingdue to two tones of slightly different
  frequency
• Arises from interference
• Two slightly mismatched tuning forks
  compressions and rarefactions are periodically in
  step, then out of step

Maximum sound
Minimum sound
18
Beats

• Beat frequency can be found by taking the
  absolute value of the difference between the two
  frequencies of the interacting waves
• Overall tone (pitch) heard frequency average
• Useful for
• tuning musical instruments listen for beats to
  disappear when frequencies of instrument
  identical to a standard (tuning fork).
• Beats produced when incident wave interferes with
  a reflected wave from a moving object reflected
  wave has Doppler-shifted frequency, so the two
  waves differ slightly in freq. Hear beats.
• That underlies how police radar in
  speed-detectors work, since Doppler shift, and
  beat freq, is related to speed of car.
• Also underlies how dolphins use beats to sense
  motions

http//www.jburroughs.org/science/mschober/soundmu
sic/sframe.htm
19
Beats

• A violinist tuning her violin, plays her A-string
  while sounding a tuning fork at concert-A 440 Hz,
  and hears 4 beats per second. When she tightens
  the string (so increasing its frequency), the
  beat frequency increases. What should she do to
  tune the string to concert-A, and what was the
  original un-tuned frequency of her string?
• Beat frequency 4 Hz, so original frequency is
  either 444 Hz or 436 Hz. Increasing frequency
  increases beat frequency, so makes the difference
  with concert-A greater. So original frequency
  must have been 444 Hz, and she should loosen the
  string to tune it to concert-A.
• A human cannot hear sound at frequencies above 20
  000 Hz. But if you walk into a room in which two
  sources are emitting sound waves at 100 kHz and
  102 kHz you will hear sound. What beat frequency
  do you hear? Why can you hear this?
• You are hearing the (much lower) beat frequency,
  2 kHz 2000 Hz.

20
Waves in Strings Pipes

• When a string is plucked a wave (standing) will
  reflect back and forth.
• The frequency of the standing wave depends on the
  number of antinodes, the wave speed and the
  length of the string
• n number of antinodes
• v wave speed
• L string length

? 2L
First harmonic (fundamental frequency)
? 1/2L
? L
? 2/3L
21
Waves in String Pipes

• An orchestra tunes up for a big concert by
  playing an A, which resounds with a fundamental
  frequency of 440. Hz. Find the first and second
  overtones of this note.
• Zeke plays a C on his guitar string, which
  vibrates with a fundamental frequency of 261 Hz.
  The wave travels down the string with a speed of
  400. m/s. What is the length of the guitar
  string?
• Would Zeke need longer or shorter strings to play
  the fundamental frequency for higher notes?

22
Waves in Strings Pipes

• Waves in pipes that are open at both ends behave
  much like waves in strings.
• Antinodes always form at the open ends of a pipe
• Nodes always form at the closed ends
• If a pipe is open at both ends the possible
  frequencies are
• If a pipe is closed at one end, the possible
  frequencies are

where n 1, 2, 3, for other overtones
where n 1, 3, 5, for other overtones
http//www.physics.smu.edu/olness/www/03fall1320/
applet/pipe-waves.html
23
Waves in Strings Pipes

• Max blows across the opening of a partially
  filled 20.0 cm high soft drink bottle and finds
  that the air vibrates with a fundamental
  frequency of 472 Hz. How high is the liquid in
  the bottle?
• A train passes through a tunnel that is 550 m
  long. What is the fundamental frequency of the
  vibrating air in the tunnel?