Wave Interference

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Wave Interference

• Chapter 8.3

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Why would we need to know the speed of a wave
anyway???

• To predict when a tsunami will strike the shore.
• To determine the epicentre of an earthquake. To
  do this, seismologists look at the difference in
  time it takes for a P-wave to reach a location
  and an S-wave to reach a location.

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Reading Seismographs

• Which city is farthest from the earthquake?
• Which city is closest to the earthquake?
• How do you know?

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Natural Frequency

• A pendulum or spring (wave) has a natural
  frequency the speed at which it vibrates
  freely.
• The frequency depends on the length and tension
  of the medium . Shorter springs and pendulums
  have higher natural frequencies than longer ones.
  
• Example Guitar Strings we shorten the strings
  to change the note (ie the frequency that the
  string vibrates naturally)
• To tune a guitar we tighten the strings or loosen
  them to get them to vibrate at the correct
  frequency (note).

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Try This

• Get 3 pop bottles and fill each with a different
  amount of water. Why do they make different
  sounds?
• Because the air is shortened so it vibrates at
  a different frequency!

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Resonance

• Phenomena that occurs when energy is added to a
  vibrating system at the same frequency as its
  natural frequency.
• Resonance makes the amplitude of the vibrations
  become larger.
• The waves interact with each other and add
  together.
• Example When you push someone on a swing or use
  their legs to push at the same frequency (at the
  natural frequency) they will go higher! This is
  because energy is added. The vibrations and your
  push are IN PHASE.

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Summary

• Natural Frequency the speed at which something
  vibrates at naturally. It depends on properties
  of the medium (length, tension).
• Ex Guitar strings have a natural frequency that
  corresponds to a note.
• Resonance - Phenomena that occurs when energy is
  added to a vibrating system at the same frequency
  as its natural frequency. Amplitude (and energy)
  increases.
• Ex Using your legs on a swingset to go higher.

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Resonance Examples

• Bay of Fundy Tides
• When a choir sings
• Shattering of glass (http//www.youtube.com/watch
  ?v17tqXgvCN0E )
• http//www.youtube.com/watch?vWFbUpUE9KiUfeature
  related
• Allows us to pick up TV/radio signals (electrical
  resonance)
• MRIs Magnetic Resonance Imaging (magnetic field
  allows doctors to look inside you!)
• http//www.youtube.com/watch?vH0adTNhzGxU
• Your car going at a certain speed starts to
  vibrate! (poor wheel alignment)
• Tacoma Narrows Bridge (video from before!) wind
  was IN PHASE with natural frequency of bridge

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In Phase

• In Phase - Two waves with the same frequency are
  in phase if their crests and troughs occur at the
  same time.

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Out of Phase

• When two waves with the same frequency are not
  in sync.
• http//boingboing.net/2011/05/13/beautiful-out-of-
  pha.html

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In Phase/Out of Phase Example

• If I drop two rocks in water and they produce
  waves with the same frequency, there are some
  places where the waves arrive in phase. This
  means that two crests arrive at the same time.
  The two crests move the water upwards to make a
  larger wave.
• In other places, the waves will arrive out of
  phase. When a crest arrives from one rock, a
  trough arrives from the other rock. This time,
  the effect of the waves cancel each other out.
  The water does not move at all.

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Wave Interference

• The speed of a wave does not depend on the
  amplitude or frequency. It depends on the
  properties of the medium in which it travels.
• Although a wave with a larger amplitude transfers
  more energy, it moves with the same speed as a
  smaller amplitude wave through a given medium.
• As long as the material is the same, the speed of
  high and low frequency waves is the same.

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Wave Interference

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

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Types of Interference

• Constructive Interference (in phase)
• When 2 crests arrive at the same time (or 2
  troughs) OR at any point where the waves add
  together to make a larger wave (temporary)

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Constructive Interference
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Partial Constructive Interference
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Types of Interference

• Destructive Interference (out of phase)
• 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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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
• Cool example of interference.

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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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Labs!
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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!)

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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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Try This

• Get a cup of water
• Get a few different tuning forks
• Strike the tuning fork. You cant see the air
  move.
• Put the vibrating tuning fork in the water. What
  happens?

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Think about.

• When you were a child, did you play telephone?
• Heres how it works Using 2 cups, attach a
  string from 1 cup to the other.
• What happens if you talk in one cup?
• Explain why the other person can hear!

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How does a record work?

• http//www.videojug.com/interview/fun-science-demo
  nstrations
• 2nd section

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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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Starter

• What is the relationship between the amplitude of
  a wave and the energy carried through the wave?
• When a wave reaches the boundary of a new medium,
  part of the wave is reflected and part
  transmitted. What determines the comparative
  sizes of the reflective and transmitted wave?
• A pulse reaches the boundary of a new medium more
  dense than the one from which it came. Is the
  reflected pulse erect or inverted?

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Answers

1. The bigger the amplitude of the wave, the more
   energy the wave has.
2. The type of medium and how different it is.
   Example A hard wall vs a soft/padded wall. The
   hard wall will reflect more of the wave than the
   soft wall (which will absorb more). If a wave
   goes from more dense to less dense, the
   amplitude/energy will be more in the transmitted
   wave than the reflected wave and vice versa.
3. Inverted

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• 4) Waves are sent along a spring of fixed
  length.
• a) Can the speed of the waves in the spring be
  changed? Explain.
• b) Can the frequency of a wave in the spring be
  changed? Explain.
• 5) You repeatedly dip your finger into a sink
  full of water to make circular waves. What
  happens to the wavelength, velocity, and
  frequency as you move your finger faster?

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Answers

• 4) a) No. Since the spring is of fixed length,
  the medium cannot be changed. Since the speed of
  waves depends on the medium, the speed cannot be
  changed.
• B) Yes, the frequency of the wave can be changed
  by producing more or fewer waves each second.
• 5) Wavelength decreases, since the waves are
  being created closer together.
• Velocity stays the same, since the medium has
  not changed.
• Frequency increases, since you are creating
  more waves every second

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Questions for You!

• Page 343, questions 3, 4, 6, 7