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1145
Chapter 15
Wave Motion
Conceptual Problems
*1
•
Determine the Concept
The speed of a transverse wave on a rope is given by
µ
F
v
=
where
F
is the tension in the rope and
is its linear density. The waves on the
rope move faster as they move up because the tension increases due to the weight of the
rope below.
2
•
Determine the Concept
The distance between successive crests is one wavelength and
the time between successive crests is the period of the wave motion. Thus,
T
= 0.2 s and
f
= 1/
T
=
5 Hz.
correct.
is
)
(
b
3
•
Picture the Problem
True. The energy per unit volume (the average energy density) is
given by
2
0
2
2
1
av
s
ρω
η
=
where
s
0
is the displacement amplitude.
4
•
Determine the Concept
At every point along the rope the wavelength, speed, and
frequency of the wave are related by
.
f
v
=
λ
The speed of the wave, in turn, is given
by
F
v
=
where
F
is the tension in the rope and
is its linear density. Due to the
weight of the rope below, the tension is greater at the top and the speed of the wave is
also greater at the top. Because
v,
∝
the wavelength is greater at the top.
*5
•
Determine the Concept
The speed of the wave
v
on the bullwhip varies with the tension
F
in the whip and its linear density
according to
F
v
=
. As the whip tapers, the
wave speed in the tapered end increases due to the decrease in the mass density, so the
wave travels faster.
6
•
Picture the Problem
The intensity level of a sound wave
β
,
measured in decibels, is
given by
()
0
log
dB
10
I
I
=
where
I
0
= 10
12
W/m
2
is defined to be the threshold of
hearing.
Express the intensity of the 60dB
sound:
0
60
log
dB
10
dB
60
I
I
=
⇒
0
6
60
10
I
I
=
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View Full DocumentChapter 15
1146
Express the intensity of the 30dB
sound:
()
0
30
log
dB
10
dB
30
I
I
=
⇒
0
3
30
10
I
I
=
Because
I
60
= 10
3
I
30
:
false.
is
statement
The
7
•
Determine the Concept
No.
Because the source and receiver are at rest relative to each
other, there is no relative motion of the source and receiver and there will be no Doppler
shift in frequency.
8
•
Determine the Concept
Because there is no relative motion of the source and receiver,
there will be no Doppler shift and the observer will hear sound of frequency
f
0
.
correct.
is
)
(
a
*9
••
Determine the Concept
The light from the companion star will be shifted about its mean
frequency periodically due to the relative approach to and recession from the earth of the
companion star as it revolves about the black hole.
10
•
Determine the Concept
In any medium, the wavelength, frequency, and speed of a wave
are related through
λ
=
v
/
f
. Because the frequency of a wave is determined by its source
and is independent of the nature of the medium, if
v
differs in the two media, the
wavelengths will also differ. In this situation, the frequencies are the same but the speeds
of propagation are different.
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 Spring '07
 Licini

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