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.
1.
A mass on a spring undergoes simple harmonic motion.
The speed of the mass is
given by the following expression:
(a)
What is the frequency of the mass's motion?
(b)
What is the total energy of the harmonic oscillator?
Solution:
(a)
The angular frequency is 12.6s
1
, so the frequency is 12.6s
1
/ 2
π
= 2.01s
1
.
(b)
The total energy is equal to the kinetic energy when the speed is at its maximum
value, since the potential energy there is zero.
The maximum speed is 0.35m/s.
Thus
,
E = 1/2 Mv
2
MAX
= (0.0613m
2
/s
2
)
M
.
Due to a typo, the mass
M
is missing from the problem statement; it's supposed to be
0.10
kg
.
It's OK to just leave it as
M
, and if this mistake was discovered during the actual
final, we would just announce a correction and write the value of
M
on the board.
2.
A string with a mass per unit length of 0.050
kg/m
is tied down at both ends, 1 meter
apart, and held under tension.
The fundamental frequency of the string is 120
hz
.
(a)
What is the 5th harmonic frequency?
(b)
What would be the fundamental frequency if the tension was doubled?
Solution:
(a)
The 5th harmonic frequency is just 5 times the fundamental, so it is 600
hz
.
(b)
The fundamental frequency is proportional to the square root of the tension, so
increasing the tension by a factor of 2 would increase it by a factor of sqrt(2).
The new
fundamental frequency would be 120 sqrt(2) = 170
hz
.
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A jet aircraft flying 300 meters overhead produces a sound intensity level of 110
decibels on the ground.
What is the total power produced in sound waves, in watts?
(a)
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 Spring '07
 Smith
 Particle Physics, Electron, Energy, Mass, Work

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