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Proof that
f
(
x ±
v
t
)
solves the wave equation
Write
f
(
x
±
v
t
)
as
f
(
u
)
, where
u = x ±
v
t
.
So
and
Now, use the chain rule:
So
⇒
and
⇒
Substituting into the wave equation:
1
u
x
∂
=
∂
v
u
t
∂
= ±
∂
f
f
u
x
u
x
∂
∂ ∂
=
∂
∂
∂
f
f
u
t
u
t
∂
∂ ∂
=
∂
∂
∂
f
f
x
u
∂
∂
=
∂
∂
v
f
f
t
u
∂
∂
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This note was uploaded on 02/16/2011 for the course PHYS 2163 taught by Professor Briscoe during the Fall '10 term at GWU.
 Fall '10
 briscoe
 Physics

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