Wave Interference

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Wave Interference

• Chapter 8.3

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Interference

• What happens when 2 waves pass through the same
  region of space at the same time

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Types of Interference

• Constructive Interference
• When 2 crests arrive at the same time (or 2
  troughs)
• The 2 crests move the wave upwards to make a
  larger wave (temporary)
• Destructive Interference
• When 1 crest and 1 trough arrive at the same time
  and cancel each other out if they are identical
  in size (temporarily).
• Partially destructive waves may not cancel each
  other but dampen the wave temporarily.

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Constructive Interference
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Destructive Interference
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Constructive Destructive
Partially Destructive
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Interference
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Interference
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Interference
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Interference
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• http//www.youtube.com/watch?vXqo6sEt1cUE

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Quick Quiz

• 1. Several positions along the medium are labeled
  with a letter. Categorize each labeled position
  along the medium as being a position where either
  constructive or destructive interference occurs.

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Answers

• Constructive Interference G, J, M and N
• Destructive Interference H, I, K, L, and O

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How is this similar to crashes???How is it
different???

• Momentum
• Energy

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Principle of Superposition

• In the region where the waves overlap, the result
  and displacement is the algebraic sum of their
  separate displacements.
• NOTE A crest is positive and a trough is
  negative!
• NOTE Waves do not change shape or size when
  they meet. They can pass through each other.
  However, when they overlap, a different shaped
  wave emerges temporarily!

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Example of Superposition

• If one wave has an amplitude of 3cm and the
  other wave has an amplitude of -6cm, the
  resultant displacement is
• -3cm.

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Example 2 of Superposition

• If one wave has an amplitude of 3cm and the
  other wave has an amplitude of 6cm, the
  resultant displacement is
• 9cm.
• See page 355 for diagrams!

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Superposition of Waves
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Superposition of Waves
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Superposition of Waves
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Questions for You

• Page 362 1, 2, 3 (use graph paper for this
  one!)
• Worksheet

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Answers

• 1. Constructive interference amplitude at
  superposition is 4 cm (2 2).
• 2. Destructive interference - cancel out (2
  -2 0).
• 3. Principle of Superposition states that the
  displacement is the sum of the separate
  displacements

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Standing Waves

• When two pulses with equal but opposite
  amplitudes meet.
• The waves have the same shape, amplitude and
  wavelength but opposite directions.

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Node

• You can find points in the medium that are
  completely undisturbed at all times (destructive
  interference).
• A point where disturbances caused by two or more
  waves result in no displacement.
• MATH 11 On the SA!
• http//en.wikipedia.org/wiki/FileStanding_wave.gi
  f

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Antinode

• You can find one point that undergoes the
  greatest displacement.
• Point of maximum displacement of two superimposed
  waves (constructive interference)
• Occur at crests and troughs.
• Occur halfway between nodes.

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• There are nodes at the end of a rope and
  antinodes in the middle.
• The resulting wave appears to be standing still.
  This is a standing wave.
• http//www.physicsclassroom.com/mmedia/waves/harm4
  .cfm

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Page 357
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Page 357
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How do we get a standing wave?

• Have one vibrating source.
• The second wave is actually the reflected wave
  from the incident wave
• Example Violin strings
• Waves move toward the fixed ends of the violin.
  When they reach the ends, the waves reflect back.
  There is interference. Standing waves form if
  nodes occur at the ends of the string/violin.
  This occurs if the strings are vibrating at the
  resonance frequency.

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Animation

• http//www.physicsclassroom.com/Class/waves/u10l4c
  .cfm

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Questions for You

• Page 362
• 4, 5

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Answers

• 4. You would see nodes evenly spaced and
  antinodes (as crests and troughs at the same
  time) evenly spaced between the nodes. It is
  called a standing wave because the nodes are not
  moving.

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• 5. The nodes are distributed at distances of
  half the wavelength (as are the antinodes). The
  antinodes are spaced evenly between these. Nodes
  are on the equilibrium or sinusoidal axis.
  Antinodes are found at troughs and crests.
• Nodes are caused by destructive interference.
  Antinodes are caused by constructive interference.

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Wave Properties Worksheet

• Part of a wave questions 1 to 10
• Wave Boundaries and Interference questions 11
  to 15, 17
• We will cover 16 next day!