Wave Interference
Chapter 8.3
Interference
• What happens when 2 waves pass
through the same region of space at the
same time
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.
Constructive Interference
Destructive Interference
Constructive
Destructive
Partially
Destructive
Interference
Interference
Interference
Interference
• http://www.youtube.com/watch?v=Xqo6sEt
1cUE
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.
Answers
• Constructive Interference: G, J, M and N
• Destructive Interference: H, I, K, L, and O
How is this similar to crashes???
How is it different???
• Momentum
• Energy
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!
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.
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!
Superposition of Waves
Superposition of Waves
Superposition of Waves
Questions for You
• Page 362 – 1, 2, 3 (use graph paper for
this one!)
• Worksheet
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
Standing Waves
• When two pulses with equal but opposite
amplitudes meet.
• The waves have the same shape,
amplitude and wavelength but opposite
directions.
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/File:Standing_wave.g
if
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.
• 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
Page 357
Page 357
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.
Animation
• http://www.physicsclassroom.com/Class/w
aves/u10l4c.cfm
Questions for You
• Page 362
• 4, 5
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.
• 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.
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!