Vibrations & Waves & Sound

1
Vibrations Waves Sound

• a periodic motion of the particles of an
  elastic body or medium in alternately opposite
  directions from the position of equilibrium when
  that equilibrium has been disturbed
• When things vibrate, they move the air and create
  sound waves
• Music, talking, sirens, etc.

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Vibrations Waves
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Transverse Waves

• Wave Anatomy

crest
trough
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Vibrations Waves

• Wavelength - Distance between peaks
• Amplitude - Max Height above resting spot
• Frequency - Number of Nodes-Crests-Troughs/second
• Period - Time of a complete vibration
• Period 1 / Frequency
• Frequency 1 / Period

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Vibrations Waves

• Water Waves bounce swimmers up and down
• Sound Waves - move air back and forth

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Wave Motion

• Consider a pebble thrown in the water
• Creates circular waves that move out from the
  disturbance
• Water moves up and down, the wave moves outward
  away from the disturbance
• Waves carry energy from the impact
• A bug in the water will move and and down

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Wave Speed
Wavelength is distance between peaks Frequency is
number of peaks per second going past a point in
the water Frequency depends on wavelength and how
fast the wave moves!!!
Speed Wavelength x Frequency
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Longitudinal or Transverse?
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Longitudinal Waves

• Wave Anatomy

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Sound Waves
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Human Hearing
sound wave
vibrates ear drum
amplified by bones
converted to nerve impulses in cochlea
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Sound Waves
Molecules in the air vibrate about some average
position creating the compressions and
rarefactions. We call the frequency of sound the
pitch.
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Human Hearing

• Pitch
• highness or lowness of a sound
• depends on frequency of sound wave
• human range 20 - 20,000 Hz

ultrasonic waves
subsonic waves
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B. Human Hearing

• Intensity
• volume of sound
• depends on energy (amplitude) of sound wave
• measured in decibels (dB)

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Human Hearing
DECIBEL SCALE
120
110
100
80
70
40
18
10
0
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Sound Waves
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Speed of Sound

• Depends on the material of the vibrating medium
• Sound can vibrate water, wood (speaker
  enclosures, pianos), metal, plastic, etc.
• Sound speed in dry air is 330 meters/second at 0o
  C
• Faster in warm air, slower in cold
• Water 4 times faster, steel 15 times faster

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Wave Reflection

• When a sound wave reflects from a surface we
  generate an echo
• Wave reflection from surfaces depends on the
  characteristics of the surface
• Smooth hard surfaces reflect best
• Rough soft surfaces reflect poorly
• Energy not reflected is absorbed or transmitted
  through the material

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Wave Reflection

• Think of arrows pointing in the direction of the
  wave motion
• We can trace the path of these arrows

Angles Equal
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Wave Reflection
Acoustics of room design is very interesting.
Need some reflections to liven the room. Too
many reflections and the sound gets mushy. Look
in a concert hall or auditorium to see the
different sound treatments
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Wave Refraction

• If there is a change in the characteristics of a
  medium, waves are bent
• This occurs because different parts of the wave
  front travel at different speeds
• Think of a marching around a curved track
• The inside people have to move more slowly than
  the outside people to keep the lines straight

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Wave Refraction
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Wave Reflection Refraction

• The combination of reflection and refraction
  enables imaging
• Ultrasonic medical imaging
• Naval SONAR for detecting submarines
• Bats catch mosquitoes
• Catch discussion of dolphins on p. 261

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Natural Frequencies

• Objects have natural frequencies based on their
  size and structure
• Guitar strings are an example
• Timpani heads
• Air columns

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Forced Vibrations

• Can externally impose a vibration on an object
• Guitars and violins and pianos
• Set the wood into motion at the frequency of the
  string
• This provides a larger surface to interact with
  the air
• Harp vs. Piano

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Resonance

• When the forced vibration matches a natural
  frequency we get a resonance condition
• Think about a swing on a playground
• You go high when you pump the swing at its
  natural vibration frequency
• Sympathetic vibrations in tuning forks
• Famous Tacoma Narrows bridge collapse

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Next Time

• We continue the chapter on waves and sound.

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Wave Interference

• Principle of Superposition
• Works for both longitudinal waves and for
  transverse waves

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Wave Interference

• Simply align the waves in time and add the
  amplitudes
• Amplitudes can be either positive or negative
• If the amplitudes are of the same sign, the wave
  is reinforced and grows bigger
• If the amplitudes are of opposite sign, the wave
  is diminished and grows smaller

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Wave Interference
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Wave Interference
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Wave Interference

• So far, we have only looked at waves that have
  the same wavelength or frequency
• What happens if the frequencies are different?
• According to the Superposition Principle, we
  simply add the two waves together to see what
  results

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Wave Interference

• Produces Beats
• This is how musicians tune their instruments to
  match in the orchestra

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Wave Interference
10 Frequency Difference
20 Frequency Difference
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Standing Waves
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Standing Waves
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C. Doppler Effect

• Doppler Effect
• change in wave frequency caused by a moving wave
  source

• moving toward you - pitch sounds higher
• moving away from you - pitch sounds lower

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Doppler Effect
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Wave Barriers
The object is moving at the speed of waves in the
medium. See how the waves pile up at the source.
40
Shock Waves
The source is moving faster than the wave speed
in the medium. A shock wave is formed and it is
very difficult to break through the previous wave
barrier. These waves produce sonic booms.
41
Music vs. Noise

• Music
• specific pitches and sound quality
• regular pattern
• Noise
• no definite pitch
• no set pattern

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Guitar Strings
43
Guitar Strings
A combination wave composed of the 1st harmonic
and the third harmonic.
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Music

• What makes instruments unique is the combination
  of harmonics produced by the different
  instruments.
• Flutes produce primarily the 1st harmonic
• They have a very pure tone
• Oboes produce a broad range of harmonics and
  sound very different

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Combining Waves Revisited
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Combining Waves
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Musical Instruments

• Three ways to make sound
• Vibrate a string
• Vibrate an air column
• Vibrate a membrane

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Vibrating Strings

• Violin, viola, cello, string bass
• Guitars
• Ukuleles
• Mandolins
• Banjos
• All vibrate a structure to amplify the sound

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Vibrating Air Columns

• Pipe Organs
• Brass Instruments
• Woodwinds
• Whistles

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Vibrating Membranes

• Percussion Instruments
• Snare Drum
• Bass Drum
• Bongos
• Timpani are unique in that they are tuned to
  produce particular 1st harmonics
• You see the timpanist tunes each drum during a
  performance