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Physics 214 Problem Set #4
(Due 11:15 am, Thursday 9/25/08)
1.
In lecture, we showed that the displacement
s
(
x
,
t
) in a onedimensional sound wave satisfies
the wave equation:
22
2
2 2
//
st
sx
∂∂
=∂∂
v
, where
2
/
B
ρ
=
v
.
Starting with the wave
equation for
s
(
x
,
t
) and the relationship between pressure and displacement, show that
pressure variation
p
(
x
,
t
) must also satisfy a wave equation of the same form with the
same wave speed:
2
p
tp
x
=
v
. Therefore, we can equally well describe a 1D
sound wave using
s
(
x
,
t
) or
p
(
x
,
t
).
[Hint: take
/
x
∂ ∂
of both sides of the wave equation for
s
(
x
,
t
).]
2.
Consider a spring that obeys Hooke's law with spring constant
κ
, total mass
M
, and relaxed
(unstretched) length
L
0
. The spring is stretched to a length
L
>
L
0
and its ends attached to
keep it under tension. We want to derive the wave equation for
longitudinal
waves on the
spring and to find the wave speed.
Consider
,
M
,
L
0
, and
L
to be known quantities.
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 Fall '07
 GIAMBATTISTA,A
 Physics

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