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Standing Waves
Physics 202Professor Lee
CarknerLecture 7
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PAL #6 Wave Energy How do you find linear density?
v = f = (/)½ or = /f22
Get frequency from function generator f =
Get wavelength by measuring on string =
Get tension from hanging weights hanging mass is 225g so = mg = (.225)(9.8) =
2.205 N =
Velocity = f v = (22.54)(1.5) =
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Exam #1 Friday About 1/3 multiple choice
Study notes Study Quizdom questions Look at textbook “Checkpoint”
questions About 2/3 problems
Study PAL’s and SuperPALS Study old homework Do new practice homework questions
Try to do this with just equation sheet
Need (real) calculator and pencil
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Standing Waves
The two waves will interfere, but if the input waves do not change, the resultant wave will be constant
Nodes --
Antinodes -- places where the amplitude is a maximum (only place where string has max or min displacement) The positions of the nodes and antinodes do not change,
unlike a traveling wave
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Standing Wave Amplitudes
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Equation of a Standing Wave
If the two waves have equations of the form:
Then the sum is:
The amplitude varies with position e.g. at places where sin kx = 0 the amplitude
is always 0 (a node)
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Nodes and Antinodes
For kx = n, sin kx = 0 and y = 0 Node:
x=n (/2)
For kx=(n+½), sin kx = 1 and y=2ym
Antinode:x=(n+½) (/2)
Antinodes also occur every 1/2 wavelength, but at a spot 1/4 wavelength before and after the nodes
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Resonance Condition
Standing waves occur due to resonance
When do you get resonance?
You must have: An integer number of “loops”
Since each “loop” is half a wavelength
= 2L/n where n = 1,2,3,4,5 …
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Resonance?
Under what conditions will you have resonance? Solve for n, must be integer
v = ()½ = f Can find new in terms of old and see if
it is an integer fraction or multiple
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Harmonics
f=(nv/2L) For a string of a certain length that will have waves of
a certain velocity, this is the frequency you need to use to get strong standing waves
The number n is called the harmonic number
For cases that do not correspond to the harmonics the amplitude of the resultant wave is very low (destructive interference)
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Generating Harmonics Many devices are designed to produce
standing waves e.g.,
Frequency corresponds to note e.g.,
Can produce different f by changing v
Changing L
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Next Time
Test #1 For Monday, December 5
Read 17.1-17.4 and do webassign homework
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What kind of string propagates waves the fastest?
a) Heavy and tightb) Heavy and loosec) Light and loosed) Light and tighte) We can’t know wave speed without
knowing the input frequency
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How would you modify the wave generator to input the maximum amount of energy?
a) Increase frequency, increase amplitude
b) Increase frequency, decrease amplitudec) Decrease frequency, increase amplituded) Decrease frequency, decrease amplitude e) Input energy is independent of frequency
and amplitude
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What kind of string transmits energy the fastest?
a) Heavy and tightb) Heavy and loosec) Light and loosed) Light and tighte) All strings transmit energy at the same
rate
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Consider a wave traveling along a string that can be combined with three otherwise identical waves with phase shifts of 0.5, 1.0, and 1.9 radians. Rank the resulting wave by amplitude, largest first.
a) 0.5, 1.0, and 1.9 b) 1.9, 1.0, 0.5c) 1.0, 0.5, 1.9d) 1.9, 0.5, 1.0e) 0.5, 1.9, 1.0