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Physics 214 Problem Set #3
(Due 11:15 am, Thursday 9/18/08)
1.
A transverse wave on an ideal string (no forces other than tension) is described by
y
(
x,t
) =
A
e
i
(
kx
+
ω
t
)
where
A
= (–0.35 mm) –
i
(0.20 mm),
ω
= 2510 rad/s, and
k
= 50.2 rad/m.
The mass per unit
length is 0.025 kg/m.
(Taking the real part to obtain
y
(
x,t
) is understood.)
(a) Sketch a snapshot (a graph of
y
vs.
x
) of the string at
t
= 0, with numerical values on the
axes. Show at least two complete cycles.
Identify one point on your graph for each of the
following conditions: maximum particle velocity upward, zero particle velocity, maximum
particle acceleration downward, and zero particle acceleration. Give the numerical values of the
maximum velocity and acceleration.
(b) What are the wave speed and direction of propagation?
(c) What is the maximum vertical force on a segment of string due to the neighboring segment
on the left (force exerted
on one side only
, not the net force)?
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 Fall '07
 GIAMBATTISTA,A
 Force, Mass, 1 mm, 0.025 kg, 0.20 mm, 0.35 mm, 50.2 rad

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