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Physics 214 Assignment 5
Concepts:
Boundary conditions
Fourier analysis
Reflection and Transmission of waves
Superposition
Reading:
AG Notes on Superposition and Standing Waves (from website); Y&F, Vol. 1,
Chapter 16
Assignment:
Due in lecture on Tuesday, February 26.
Please turn in this sheet stapled to the top of your work.
1.
(a) Consider standing waves on a string of length L that is fixed at both ends.
How far are
(i) the first node and (ii) the first antinode from the fixed end?
(b) Now consider a string of length L that has one fixed end and one ideal free end
(implmented using a massless slip ring.) How far are (i) the first node and (ii) the first
antinode from the fixed end?
(c) It's very hard to make an ideal free end.
But fixed ends are easy.
Using some extra rope
and a fixed end, how might you create the standing wave pattern you'd get from a rope of
length L with one free end?
2. At
t
= 0, the wave pulses shown below are moving away from one another. The wave
speed is 5 m/s. The left end (
x
= 0) is free (massless slip-ring boundary condition) and the
right end (
x
= 25 m) is fixed.
0
1
2
3
4
5
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
x (m)
y
(cm)
Free End
(a) Draw the left end of the string (0
≤
x
≤
4 m) at
t
= 1.2 s.
(b) Draw the right end of the string (21 m
≤
x
≤
25 m) at
t
= 2.0 s.
(c) Draw the velocity distribution (a graph of
/
y
t
∂
∂
as a function of
x
) at
t
= 4.2 s for the part of
the string where the velocity is nonzero.
Physics 214, Spring 2008
1
Cornell University

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