Physics 2 Class 16 Wave superposition, interference, and reflection

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Physics 2Class 16Wave superposition,
interference, and reflection
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Adding waves superposition

• When two waves are incident on the same place at
  the same time, their amplitudes can usually just
  be added.
• In the next few slides we will look at some
  special cases (both with two waves at the same
  frequency and with the same amplitude)
• same frequency and amplitude
• superposition at a point in space
• same direction, but different phase
• opposite directions

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Adding waves

• In most simple systems, the amplitude of two
  waves that cross or overlap can just be added
  together.

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Adding two equal amplitude waves at a point
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iClicker check 16.1

• For which phase difference ? is the superposition
  amplitude a maximum?
• ?0
• ??/2
• ? ?

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iClicker check 16.2

• For which phase difference ? is the superposition
  amplitude a minimum?
• ?0
• ??/2
• ? ?

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Adding two waves that have the same frequency and
direction, but different phase

• What happens when the phase difference is 0?
• What happens when the phase difference is ?/2?
• What happens when the phase difference is ??

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• Constructive interference when ?0.
• Destructive interference when ??.

Link to animation of two sine waves adding in and
out of phase (Kettering)
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What happens when a wave is incident on an
immovable object?

• It reflects, travelling in the opposite direction
  and upside down.

(Now watch patiently while your instructor plays
with the demonstration.)
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Same frequency, opposite directions

• What happens when kx is 0?
• What happens when kx is ?/2?
• What happens when kx is ??

Link to animation of two sine waves traveling in
opposite directions
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Standing waves

• Interfering waves traveling in opposite
  directions can produce fixed points called nodes.
• y1 ym sin(kx wt)
• y2 ym sin(kx wt)
  vw/k
• yT y1 y2 2ym cos(wt) sin(kx)
• yT0 when kx 0, p, 2p...
• yT(t)maximum when kx p/2, 3p/2, 5p/2 ...

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Standing waves - ends fixed

• Amplitude will resonate when an integer number of
  half-wavelengths fit in the opening.
• Example violin

l2L/n
5th harmonic, n 5
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Both Ends Fixed
Once again, watch patiently while your instructor
plays with the string.
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Standing waves - one end free

• Free end will be an anti-node at resonance.
• Demo spring (slinky) with one end free.

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One End Open (e.g. Organ Pipe)
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Standing waves - both ends free
Example wind instrument
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Both Ends Open (e.g. Organ Pipe)