Wave Interference

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Wave Interference

• For complete destructive interference to occur,
  two pulses must have
• the same ____________________
• and equal magnitude but opposite direction
• ________________

2
Wave Interference

• For complete destructive interference to occur,
  two pulses must have
• the same pulse width or wavelength
• and equal magnitude but opposite direction
• amplitude (height)

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The Interference of Sound Waves

• 3U Physics

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The Principle of Superposition

• Recall The Principle of Superposition, which
  states that when 2 waves interfere, the resulting
  displacement of the medium at any location is the
  algebraic sum of the displacements of the
  individual waves at that same location. Example

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Constructive Interference

• The sum of two crests is referred to as a ?
• The sum of two troughs is referred to as a ?.

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Constructive Interference

• The sum of two crests is referred to as a
  supercrest.
• The sum of two troughs is referred to as a
  supertrough.

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Destructive Interference

• Complete destructive interference results in
  nodes.

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The Effect of Interference

• An increase in amplitude indicates an increase in
  ?

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The Effect of Interference

• An increase in amplitude indicates an increase in
  energy, which for sound waves means an increase
  in the ?

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The Effect of Interference

• An increase in amplitude indicates an increase in
  energy, which for sound waves means an increase
  in the intensity or volume of the sound.

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Noise-Reduction Headphones

• Noise-reduction headphones cancel ambient sound
  by producing sound that is ½ wavelength out of
  phase with the ambient sound (this works best for
  single frequencies).

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Very Different Frequencies

• If two very different frequencies are sounded at
  the same time, the resulting interference pattern
  will be repeating and therefore sound musical
  (consonant) if the ratio between the frequencies
  is a small whole-number ratio

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Very Different Frequencies

• Frequencies in the ratio of 21 are an octave.

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Very Different Frequencies

• The resulting interference pattern will be
  non-repeating and therefore dissonant if the
  ratio between the frequencies is not a small
  whole-number ratio

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Slightly Different Frequencies

• What if we have two sources with slightly
  different frequencies?
• Sometimes the interference will be constructive
  (increased intensity) and sometimes destructive
  (decreased intensity).

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Different Frequencies

• This variation in intensity is heard as a
  variation in volume known as beats.

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Different Frequencies

• The beat frequency is equal to the difference
  between the two frequencies.
• E.g. if tuning forks of 255 Hz and 257 Hz are
  struck simultaneously, beats will be heard at a
  frequency of 2 Hz (2 per second).
• The closer the frequencies, the lower the beat
  frequency.

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Doppler and Beats Example

• A car with a siren of 550-Hz is driving toward an
  observer at a speed of 5 m/s. Another car with a
  siren of 550 Hz is parked beside the observer.
  What is the beat frequency heard by the observer?
  Assume the speed of sound in air is 344 m/s.

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Doppler and Beats Example

• A car with a siren of 550-Hz is driving toward an
  observer at a speed of 5 m/s. Another car with a
  siren of 550 Hz is parked beside the observer.
  What is the beat frequency heard by the observer?
  Assume the speed of sound in air is 344 m/s.

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Doppler and Beats Example

• A car with a siren of 550-Hz is driving toward an
  observer at a speed of 5 m/s. Another car with a
  siren of 550 Hz is parked beside the observer.
  What is the beat frequency heard by the observer?
  Assume the speed of sound in air is 344 m/s.

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Interference and the Listener

• Of course, what is heard by the listener will
  depend on the location of the listener. . . .

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2-Source Interference

• Two sources (here, two speakers) will produce an
  interference pattern.

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2-Source Interference

• Two sources (here, two speakers) will produce an
  interference pattern.
• Areas of constructive interference will
  experience an increase in volume.

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2-Source Interference

• Areas of destructive interference (the grey
  lines, called nodal lines) will experience a
  decrease in volume.

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2-Source Interference

• Auditoriums and many other public spaces are
  designed with walls (and ceilings and baffles)
  that will trap and absorb sound energy rather
  than reflect it so the reflections cannot
  interfere with the original waves and distort the
  sound.

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More Practice

• The Interference of Sound Waves
• An Inquiry Activity
• Homework Set 11 Sound Interference