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Physics 1C, Summer Session I, 2011
Final Exam
Instructions:
Do any 8 problems.
Please do all work on separate sheets of paper, and
hand in everything you want to be graded.
Clearly mark the problems that you want
graded, and box the answers.
Problem 1:
A mass on a spring oscillates with an amplitude
A
.
What is its displacement
from the equilibrium position, in terms of
A
, when the kinetic energy is equal to twice
the potential energy?
Solution:
The total energy of the spring is 1/2
kA
2
, the potential energy is 1/2
kx
2
, and therefore the
kinetic energy is 1/2
k
(
A
2
 x
2
).
When the kinetic energy is twice the potential energy,
Problem 2:
A string with mass per unit length of 0.010
kg / m
is 0.5 meters long and
tied down on both ends.
Tension is applied to the string.
(a)
What should the tension be to achieve a fundamental frequency of 440
hz
?
(b)
If this amount of tension is applied, what is the wave speed in the string?
Solution:
(a)
The fundamental frequency of a string with both ends tied down is
Solve for the tension:
(b)
The wave speed is
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View Full DocumentProblem 3:
A dolphin is swimming towards an underwater cliff at a speed of 5
m/s
.
The dolphin emits an ultrasound wave with a frequency of 100 kHz.
When the echo
returns from the cliff and interferes with the sound from the source, beats are produced.
What is the beat frequency?
Take the speed of sound in water to be 1500
m/s
.
Solution:
First find the frequency at the cliff.
In this case, we have a moving source (the dolphin)
and a stationary observer (the cliff).
If
f
S
is the frequency emitted by the dolphin, then
the frequency at the cliff is
The cliff reflects the sound at the same frequency.
But now the echo is emitted by the
cliff (a stationary source) and comes back to the dolphin (a moving observer).
The
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 Spring '07
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