Download Harmonic Oscillators and Sound Quiz

1.
A pendulum oscillates back and forth between point A and C, with
total mechanical energy (kinetic energy and relative potential energy)
of E. When the pendulum is at position B, half way from the bottom
of oscillation, which of the following would be accurate?
a. KE=0E
b. KE=.25E
c. KE=.5E
d. KE=.75E
e. KE=E
2.
A pendulum oscillates through a small angle with amplitude Θ, with a period of T. If the same pendulum
were to oscillate with amplitude Θ/2, the relative period of oscillation would be
a. T/4
b. T/2
c. T
d. 2T
e. 4T
3.
A pendulum of length L oscillates back and forth 4 times in 12 seconds. If we increased the length of the
pendulum to 4L. How many times would the pendulum oscillate back and forth in 12 seconds?
a. .5
b. 1
c. 2
d. 8
e. 16
4.
The spring is compressed and released at the position shown (x=0). A force sensor, attached to the wall
and the spring, reads force as a function of distance from position x. Only two readings are available.
When the spring is at .3m away from the compressed position the force sensor reads -6N. When the
spring is .8m away from the compressed position, the force sensor reads 9N. What is the amplitude of
the motion of the spring motion in meters?
a. .3
b. .5
c. .6
d. .7
e. .9
5.
A normal spring based oscillator has a maximum acceleration of 2m/s 2 and a mass of 4Kg, in an
environment without frictional forces. If the amplitude of motion is 8m, what is the maximum speed?
a. .5m/s
b. 2m/s
c. 4m/s
d. 8m/s
e. 16m/s
6.
Two springs of equal mass and dimensions are each dropped from some height H. Each spring bounces
off the ground and back into the air without any damping. Spring 1 has a spring constant of k, and Spring
2 has a spring constant of 2k. The maximum compression distance of spring 1 will be ____________spring
2 during impact with the ground, and the maximum height after bouncing for spring 1 will be
__________spring 2.
a. Less than, Less than
b. Less than, greater than
c. Greater than, Less than
d. Greater than, Equal to
e. Greater than, Greater than
7.
Using the graph of acceleration as a function of time for a harmonic oscillator. What is the equation for
the velocity of the harmonic
oscillator as a function of time?
(Assume the velocity at time 0 is 0)
a. V=.5sin(8t)
b. V=4sin(2t)
c. V=-12sin(2t)
d. V=-.5sin(8t)
e. V=-32sin(8t)
8.
A guitar string is plucked and the wave oscillates with speed s, wavelength λ, and frequency f. If the
tension of the string is increased the wavelength will _________ and the speed of the wave
will__________
a. Decrease, increase
b. Decrease, stay the same
c. Increase, increase
d. Stay the same, decrease
e. Stay the same, increase
9.
A spring has a mass M attached to it
while in the relaxed position. The mass
is then released and the spring is
permitted to oscillate. Which graph best
represents the amplitude of oscillation
as a function of mass added?
10. Which of the varying pendulums has the smallest frequency of oscillation? Assume each pendulum has
the same mass and the length of each pendulum is identical.
11. What is the net spring constant of the system
shown?
a. 1N/m
b. (11/18)N/m
c. (18/11)N/m
d. 4N/m
e. 11N/m
12. A ball slides back and forth in frictionless wells in the presence of gravity between points –A and A, as
shown. Which of the following motions of the ball would be closest to simple
harmonic?
13. Considering the equation of a wave moving along a string as y=4sin(2x8t), what is the speed of the wave?
a. .25
b. .5
c. 2
d. 4
e. 16
14. The power created by an speaker increases from 1watt to 10,000watts. If the observer initially
hears a sound level of 50dB at 1 watt when at 2 meters, how far away do they have to go to
hear the sound with the same intensity?
a. 16m
b. 32m
c. 64m
d. 100m
e. 200m
15. A sound emitter produces sound at a set frequency. The pitch of the
sound for the observer will be lowest at _____________ and equivalent
to the natural pitch at_____________
a. A, B and C
b. A, B and D
c. C, B and C
d. C, B and D
e. C, B and A
16. Two speakers are changed from a lower to a higher frequency of sound. Which of the following will
create a similar effect on the fringes?
a. Increasing the distance between the speakers
b. Increasing the temperature of the air
c. Increasing the wavelength emitted sound
d. (a-c)
e. None of the above
17. A space ship hovers over a black hole with a very large mass, M1. The space ship is using
thrusters to maintain its elevation (it is NOT rotating around the hole). A pendulum with a very
light chord is allowed to oscillate. The Pendulum oscillates through small angle Θ, with length L,
bob mass M2, at a distance of R from the center of the black hole.
a. Solve for period of oscillation in terms of given variables and fundamental constants (g is not a
fundamental constant, since distance from the planet is appreciably changing) (2pts)
As the distance from the center of the hole, R, is changed, and the pendulum period is recorded with the
data as shown.
b. Plot the graph of Period as a function
of distance from the center of the
black hole and determine the slope
of the graph (3pts)
c. Determine the mass contained within the black hole if the pendulum has a length of 4m.
d. If the angle of release is 10o, what is the amplitude of oscillation, A?
e. Give the velocity of oscillation as a function of time. The direction
shown is positive and the pendulum takes 2 seconds to get to
equilibrium from the position shown.
18. A 1kg object moving at a speed of 6m/s collides and sticks to the spring-mass system shown. The front
face where the 1Kg objects collides and the spring
itself are of negligible mass. The second object,
connected to the spring, has a mass of 2Kg and is
free to move away from the wall. The entire
system is frictionless. The spring behaves as a
normal spring with a constant of 100N/m.
a. What is the maximum compression
distance of the spring?
b. What is the period of oscillation of the
system?
c. What is the velocity of the center of
mass of the system after the 2kg object leaves the wall? Assume right is the positive direction,
and the 1Kg mass remains stuck to the end of the spring opposite the 2kg mass.
d. What is the acceleration of the 2kg object as a function of time? Assume time zero is the
moment the 2kg object starts to leave the wall.
e. Determine the maximum vibrational energy of the system.
19. A spring has a mass M attached to it
while in the relaxed position. The mass
is then released and the spring is
permitted to oscillate. Which graph best
represents the amplitude of oscillation
as a function of mass added?
20. Which of the varying pendulums has the smallest frequency of oscillation? Assume each pendulum has
the same mass and the length of each pendulum is identical.
21. What is the net spring constant of the system
shown?
a. 1N/m
b. (11/18)N/m
c. (18/11)N/m
d. 4N/m
e. 11N/m
22. A pendulum oscillates back and forth between point A and C, with
total mechanical energy (kinetic energy and relative potential energy)
of E. When the pendulum is at position B, half way from the bottom
of oscillation, which of the following would be accurate?
a. KE=0E
b. KE=.25E
c. KE=.5E
d. KE=.75E
e. KE=E
23. A pendulum oscillates through a small angle with amplitude Θ, with a period of T. If the same pendulum
were to oscillate with amplitude Θ/2, the relative period of oscillation would be
a. T/4
b. T/2
c. T
d. 2T
e. 4T
24. A pendulum of length L oscillates back and forth 4 times in 12 seconds. If we increased the length of the
pendulum to 4L. How many times would the pendulum oscillate back and forth in 12 seconds?
a. .5
b. 1
c. 2
d. 8
e. 16
25. The spring is compressed and released at the position shown (x=0). A force sensor, attached to the wall
and the spring, reads force as a function of distance from position x. Only two readings are available.
When the spring is at .3m away from the compressed position the force sensor reads -6N. When the
spring is .8m away from the compressed position, the force sensor reads 9N. What is the amplitude of
the motion of the spring motion in meters?
a. .3
b. .5
c. .6
d. .7
e. .9
26. A normal spring based oscillator has a maximum acceleration of 2m/s2 and a mass of 4Kg, in an
environment without frictional forces. If the amplitude of motion is 8m, what is the maximum speed?
a. .5m/s
b. 2m/s
c. 4m/s
d. 8m/s
e. 16m/s
27. Two springs of equal mass and dimensions are each dropped from some height H. Each spring bounces
off the ground and back into the air without any damping. Spring 1 has a spring constant of k, and Spring
2 has a spring constant of 2k. The maximum compression distance of spring 1 will be ____________spring
2 during impact with the ground, and the maximum height after bouncing for spring 1 will be
__________spring 2.
a. Less than, Less than
b. Less than, greater than
c. Greater than, Less than
d. Greater than, Equal to
e. Greater than, Greater than
28. Using the graph of acceleration as a function of time for a harmonic oscillator. What is the equation for
the velocity of the harmonic
oscillator as a function of time?
(Assume the velocity at time 0 is 0)
a. V=.5sin(8t)
b. V=4sin(2t)
c. V=-12sin(2t)
d. V=-.5sin(8t)
e. V=-32sin(8t)
29. A guitar string is plucked and the wave oscillates with speed s, wavelength λ, and frequency f. If the
tension of the string is increased the wavelength will _________ and the speed of the wave
will__________
a. Decrease, increase
b. Decrease, stay the same
c. Increase, increase
d. Stay the same, decrease
e. Stay the same, increase
30. A ball slides back and forth in frictionless wells in the presence of gravity between points –A and A, as
shown. Which of the following motions of the ball would be closest to simple
harmonic?
31. Considering the equation of a wave moving along a string as y=4sin(2x8t), what is the speed of the wave?
a. .25
b. .5
c. 2
d. 4
e. 16
32. The power created by an emitter increases from 1watt to 10,000watts. If the observer initially
hears a sound level of 50dB at 1 watt when at 2 meters, how far away do they have to go to
hear the sound with the same intensity?
a. 16m
b. 32m
c. 64m
d. 100m
e. 200m
33. A sound emitter produces sound at a set frequency. The pitch of the
sound for the observer will be lowest at _____________ and equivalent
to the natural pitch at_____________
a. A, B and C
b. A, B and D
c. C, B and C
d. C, B and D
e. C, B and A
34. Two speakers are changed from a lower to a higher frequency of sound. Which of the following will
create a similar effect on the fringes?
a. Increasing the distance between the speakers
b. Increasing the temperature of the air
c. Increasing the wavelength emitted sound
d. (a-c)
e. None of the above
35. A space ship hovers over a black hole with a very large mass, M1. The space ship is using
thrusters to maintain its elevation (it is NOT rotating around the hole). A pendulum with a very
light chord is allowed to oscillate. The Pendulum oscillates through small angle Θ, with length L,
bob mass M2, at a distance of R from the center of the black hole.
f. Solve for period of oscillation in terms of given variables and fundamental constants (g is not a
fundamental constant, since distance from the planet is appreciably changing) (2pts)
As the distance from the center of the hole, R, is changed, and the pendulum period is recorded with the
data as shown.
g. Plot the graph of Period as a function
of distance from the center of the
black hole and determine the slope
of the graph (3pts)
h. Determine the mass contained within the black hole if the pendulum has a length of 4m.
i.
j.
If the angle of release is 10o, what is the amplitude of oscillation, A?
Give the velocity of oscillation as a function of time. The direction
shown is positive and the pendulum takes 2 seconds to get to
equilibrium from the position shown.
36. A 1kg object moving at a speed of 6m/s collides and sticks to the spring-mass system shown. The front
face where the 1Kg objects collides and the spring
itself are of negligible mass. The second object,
connected to the spring, has a mass of 2Kg and is
free to move away from the wall. The entire
system is frictionless. The spring behaves as a
normal spring with a constant of 100N/m.
a. What is the maximum compression
distance of the spring?
b. What is the period of oscillation of the
system?
c. What is the velocity of the center of
mass of the system after the 2kg object leaves the wall? Assume right is the positive direction,
and the 1Kg mass remains stuck to the end of the spring opposite the 2kg mass.
d. What is the acceleration of the 2kg object as a function of time? Assume time zero is the
moment the 2kg object starts to leave the wall.
e. Determine the maximum vibrational energy of the system.