28
11.29
The general solution to the wave equation (Equation 11.6.10) that yields a standing wave
of any arbitrary shape can be obtained as a linear combination of standing sine waves of a
form given by Equation 11.6.14, i.e.,
()
1
2
( , )
sin
cos
sin
nnn n
n
n
x
yxt
A
t B
t
π
ωω
λ
∞
=
=+
∑
where
2
n
n
T
ω
=
since the speed of a wave is …
1
2
0
2
nn
n
n
F
v
T
λωλ
µ
==
=
we have …
1
2
0
2
n
n
F
=
But the wavelength of the standing wave is constrained by the fixed endpoints of the
string, i.e. …
2
n
l
n
=
, so …
1
2
0
n
F
n
l
=
Now, at t = 0, the wave starts from rest in the configuration specified, so…
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
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