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Standing Waves
Physics 202Professor Lee
CarknerLecture 8
PAL #7 Wave Energy
How do you find linear density? v = f = (/)½ or = /f22
Get frequency from function generator or by timing oscillator (f = 27.76 Hz)
Get wavelength by measuring on string ( = 70 cm = 0.7 m)
Get tension from hanging weights (hanging mass is 100g so = mg = (0.1)(9.8) = 0.98 N)
=0.0026 kg/m or 2.6 g/m
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
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
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
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
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
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
Standing Wave Amplitudes
Equation of a Standing Wave
y1 = ym sin (kx - t)
y2 = ym sin (kx + t) Then the sum is:
The amplitude varies with position
e.g. at places where sin kx = 0 the amplitude is always 0 (a node)
Nodes and Antinodes Consider different values of x (where n is an
integer) Node:
x=n (/2)
For kx=(n+½), sin kx = 1 and y=2ym
Antinode:
Antinodes also occur every 1/2 wavelength, but at a spot 1/4 wavelength before and after the nodes
Resonance Frequency When do you get resonance?
Since you are folding the wave on to itself
You need an integer number of half wavelengths to fit on the string (length = L)
In order to produce standing waves
through resonance the wavelength must satisfy: = 2L/n where n = 1,2,3,4,5 …
Resonance?
Under what conditions will you have resonance?
n is the number of loops on a string
v = ()½ = f Can find new in terms of old and see if
it is an integer fraction or multiple
Harmonics We can express the resonance condition in terms
of the frequency (v=f or f=v/)f=(nv/2L)
Remember v depends only on and
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)
Generating Harmonics Many devices are designed to produce
standing waves
Frequency corresponds to note
Can produce different f by changing v
Changing L
Next Time
Test #1 Next class, Monday, January 7
Read 17.1-17.4 Homework: 17.1, 17.4, 17.8
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