Phys 2214 Homework #3 Solutions
September 15, 2011
1. The disturbance travels down the rubber tube with the wave speed,
which, for a onedimensional transverse wave with constant tension
and mass/length, is given by
v
=
s
τ
μ
.
The tension
τ
is equal to the weight of the mass hanging over the
pulley, which is 10
kg
×
9
.
8
m/s
2
= 98
N
.
The linear density
μ
=
0
.
5
kg/
10
m
= 0
.
05
kg/m
. Then
v
= 44
.
3
m/s
and the time to travel
down the rubber tube is
t
=
L/v
= 10
m/
44
.
3
m/s
= 0
.
23
s
.
2. the transverse wave is given by
y
(
x, t
) = 0
.
01
m
cos
20
rad
m
x

2000
rad
s
t
!
.
(a) See the figure below, which is a plot of
y
(
x
).
According to the
Pulse Equation, the velocity of the particles in the medium is
related to the spatial slope of the wave:
∂y
∂t
=

v
∂y
∂x
,
where the minus sign is used for waves moving in the +
x
direction.
So, for (A), the maximum upward particle velocity takes place
where the slope of the wave is the most negative (see the plot).
For (B), the particle velocity is zero whenever the slope of the wave
is zero (see the plot). For (C), using the wave equation gives the
1
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 '11
 DAVIS,J.C.
 Mass, Work, Waves And Optics, vy, vph, γk, kx − ωt, τ /µ

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