PHY2061
R. D. Field
Department of Physics
chp38_10.doc
University of Florida
The Wave Equation
∂
2
22
2
2
1
0
yxt
xv
t
(,
)
)
−=
Whenever analysis of a system results in an equation of the
form given above then we know that the system supports
traveling waves propagating at speed v.
General Proof:
If
y = y(x,t) = f(xvt)
then
y
x
f
y
x
f
y
t
vf
y
t
=
′
=
′′
=−
′
=
′′
2
2
2
2
2
and
2
2
2
1
0
t
ff
)
)
′′ −
′′ =
.
Proof for Harmonic Wave:
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics

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