Wave Interference

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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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Doppler Effect
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Doppler Effect
Doppler effect occurs for all types of waves,
water, sound and even light. This is how we know
the universe is expanding.
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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.
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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.
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Waves and Music
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Guitar Strings
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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