Physics 53
Summer 2008
1
Exam III
Solutions
In questions or problems not requiring numerical answers, express the answers in terms of the
symbols given, and standard constants such as
g
. If numbers are required, use
g
= 10 m/s
2
.
Part A:
Multiple choice questions. Check the best answer. Each question has a value of 4 points.
1.
A system’s motion is described by the equation
x
(
t
)
=
A
cos
!
t
. Which of the
following is NOT true?
If
A
is independent of
the motion is simple harmonic motion.
The system starts at
t
=
0
with zero velocity.
The potential energy can be written as
U
(
x
)
=
1
2
m
2
x
2
.
√
The total force on the system is
F
=
m
2
x
. [Minus this.]
2.
For the average input power
P
av
for a driven oscillator with damping, which of
the following is NOT true?
The maximum value of
P
av
occurs when the frequency of the driving
force is equal to the frequency at which the oscillator would oscillate
freely without damping.
√
If the damping is small, the maximum value of
P
av
is less than if the
damping is large. [Larger.]
The curve of
P
av
vs.
ω
is more sharply peaked if the damping is small
than if it is large.
P
av
multiplied by the period of the oscillation is equal to the energy
dissipated by the damping in one complete oscillation.
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Summer 2008
2
3.
Two harmonic waves of the same wavelength and frequency are interfering.
Their individual intensities are
I
0
and 4
I
0
.
The minimum that the resulting intensity can be is 3
I
0
.
The second wave has 4 times the amplitude of the first wave.
√
The maximum that the resulting intensity can be is 9
I
0
. [The second wave
has twice the amplitude of the first. Constructive interference makes the
amplitude three times that of the first wave, so the intensity is 9 times.]
None of the above is true.
4.
On the piano strings for different low notes have equal length and tension, while
strings for different high notes have equal mass per unit length and tension.
Which of the following is NOT true?
√
The strings for two low notes producing 55 Hz and 110 Hz have mass per
unit lengths in the ratio 2:1. [
2
: 1
.]
Strings for high notes producing 440 Hz and 880 Hz have lengths in the
ratio 2:1.
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 Spring '07
 Mueller
 Physics, Frequency, police car, Hz

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