Question 1

By what factor should the length of a simple pendulum be changed if the period of vibration were to be two times?
​

Accepted Answer

A)   1/4
B)   0.5
C)   2
D)   4
E)   ​1.0 D

Question 2

Transverse waves travel with a speed of 100 m/s along a taut copper wire that has a diameter of 1.73 mm.What is the tension in the wire? (The density of copper is 8.93 g/cm3. )
​

Accepted Answer

A)   839 N
B)   419 N
C)   210 N
D)   105 N
E)   67 N C

Question 3

For a mass suspended on a spring in the vertical direction,the time for one complete oscillation will depend on:

Accepted Answer

A)   the value for g (the acceleration due to gravity) .
B)   the distance the mass was originally pulled down.
C)   the maximum speed of the oscillating mass.
D)   the time doesn't depend on any of the above. D

Question 4

A 0.39 kg object,attached to a spring with spring constant k = 15 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.082 m.What is its speed at the instant when its displacement is 0.041 m? (Hint: Use conservation of energy. )
​

Accepted Answer

A)   4.4 m/s
B)   8.8 m/s
C)   44 cm/s
D)   56.9 cm/s
E)   ​31.1 cm/s

Question 5

A wave is traveling in a string at 68 m/s.When the tension is then increased 15%,what will be the resulting wave speed?
​

Accepted Answer

A)   also 68 m/s
B)   73 m/s
C)   63 m/s
D)   26 m/s
E)   ​78 m/s

Question 6

Two springs,each with spring constant 10 N/m,are connected in parallel,and the combination is hung vertically from one end.A 20-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium?
​

Accepted Answer

A)   2 m
B)   0.5 m
C)   4 m
D)   1 m
E)   8 m

Question 7

A runaway railroad car,with mass 36 × 104 kg,coasts across a level track at 2.7 m/s when it collides with a spring-loaded bumper at the end of the track.If the spring constant of the bumper is 2.7 × 106 N/m,what is the maximum compression of the spring during the collision? (Assume the collision is elastic. )

Accepted Answer

A)   0.99 m
B)   1.39 m
C)   0.7 m
D)   1.88 m
E)   1.97 m

Question 8

For a wave on the ocean,the amplitude is:

Accepted Answer

A)   the distance between crests.
B)   the height difference between a crest and a trough.
C)   one half the height difference between a crest and a trough.
D)   how far the wave goes up on the beach.

Question 9

Spring #1 has spring constant 80 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective force constant of 10 N/m.What is the spring constant for Spring #2?
​

Accepted Answer

A)   70 N/m
B)   90 N/m
C)   9 N/m
D)   11 N/m
E)   ​85 N/m

Question 10

The motion of a piston in an automobile engine is nearly simple harmonic.If the 1-kg piston travels back and forth over a total distance of 11.9 cm,what is its maximum speed when the engine is running at 3,540 rpm?
​

Accepted Answer

A)   22.06 m/s
B)   11.03 m/s
C)   44.11 m/s
D)   5.51 m/s
E)   ​2.76 m/s

Question 11

An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth.A P-wave travels at 9,000 m/s and an S-wave at 4,000 m/s.If P-waves are received at a seismic station 44.2 s before an S-wave arrives,how far is the station from the earthquake center?
​

Accepted Answer

A)   159 km
B)   636 km
C)   318 km
D)   122 km
E)   ​2,210 km

Question 12

A 0.34-kg block rests on a frictionless level surface and is attached to a horizontally aligned spring with a spring constant of 55 N/m.The block is initially displaced 4.1 cm from the equilibrium point and then released to set up a simple harmonic motion.What is the speed of the block when it passes through the equilibrium point?
​

Accepted Answer

A)   2.58 m/s
B)   0.74 m/s
C)   1.82 m/s
D)   0.52 m/s
E)   ​2.35 m/s

Question 13

A car with bad shocks bounces up and down with a period of 1.62 s after hitting a bump.The car has a mass of 1,600 kg and is supported by four springs of force constant k.What is k for each spring?
​

Accepted Answer

A)   6,017 N/m
B)   1,504 N/m
C)   1,551 N/m
D)   3,009 N/m
E)   ​788 N/m

Question 14

What is the phase difference when two waves,traveling in the same medium,undergo constructive interference?

Accepted Answer

A)   270°
B)   180°
C)   90°
D)   0°

Question 15

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.4 Hz and an amplitude of 8.6 cm.If the mass of the object is 0.4 kg,what is the spring constant?
​

Accepted Answer

A)   11 N/m
B)   764 N/m
C)   306 N/m
D)   36 N/m
E)   ​657 N/m

Question 16

Bats can detect small objects such as insects that are of a size approximately that of one wavelength.If bats emit a chirp at a frequency of 60 kHz,and the speed of sound waves in air is 340 m/s,what is the smallest size insect they can detect?
​

Accepted Answer

A)   4.7 mm
B)   3.7 mm
C)   5.7 mm
D)   6.7 mm
E)   ​7.7 mm

Question 17

A wave travels in a string at 64 m/s.A second string of 25% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string?
​

Accepted Answer

A)   also 64 m/s
B)   74 m/s
C)   128 m/s
D)   57 m/s
E)   ​72 m/s

Question 18

An object is attached to a spring and its frequency of oscillation is measured.Then another object is connected to the first object,and the resulting mass is three times the original value.By what factor is the frequency of oscillation changed?
​

Accepted Answer

A)   1/3
B)   0.58
C)   1/9
D)   3
E)   ​9

Question 19

Suppose a 0.36-kg mass on a spring-loaded gun that has been compressed 0.2 m has elastic potential energy of 1.9 J.How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?
​

Accepted Answer

A)   0.54 m
B)   0.88 m
C)   0.34 m
D)   5.08 m
E)   51.52 m

Question 20

Consider two identical and symmetrical wave pulses on a string.Suppose the first pulse reaches the fixed end of the string and is reflected back and then meets the second pulse.When the two pulses overlap exactly,the superposition principle predicts that the amplitude of the resultant pulses,at that moment,will be what factor times the amplitude of one of the original pulses?

Accepted Answer

A)   0
B)   1
C)   2
D)   4

Exam 13: Vibrations and Waves

By what factor should the length of a simple pendulum be changed if the period of vibration were to be two times?

Transverse waves travel with a speed of 100 m/s along a taut copper wire that has a diameter of 1.73 mm.What is the tension in the wire? (The density of copper is 8.93 g/cm³. )

For a mass suspended on a spring in the vertical direction,the time for one complete oscillation will depend on:

A 0.39 kg object,attached to a spring with spring constant k = 15 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.082 m.What is its speed at the instant when its displacement is 0.041 m? (Hint: Use conservation of energy. )

A wave is traveling in a string at 68 m/s.When the tension is then increased 15%,what will be the resulting wave speed?

Two springs,each with spring constant 10 N/m,are connected in parallel,and the combination is hung vertically from one end.A 20-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium?

For a wave on the ocean,the amplitude is:

Spring #1 has spring constant 80 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective force constant of 10 N/m.What is the spring constant for Spring #2?

The motion of a piston in an automobile engine is nearly simple harmonic.If the 1-kg piston travels back and forth over a total distance of 11.9 cm,what is its maximum speed when the engine is running at 3,540 rpm?

An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth.A P-wave travels at 9,000 m/s and an S-wave at 4,000 m/s.If P-waves are received at a seismic station 44.2 s before an S-wave arrives,how far is the station from the earthquake center?

A car with bad shocks bounces up and down with a period of 1.62 s after hitting a bump.The car has a mass of 1,600 kg and is supported by four springs of force constant k.What is k for each spring?

What is the phase difference when two waves,traveling in the same medium,undergo constructive interference?

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.4 Hz and an amplitude of 8.6 cm.If the mass of the object is 0.4 kg,what is the spring constant?

Bats can detect small objects such as insects that are of a size approximately that of one wavelength.If bats emit a chirp at a frequency of 60 kHz,and the speed of sound waves in air is 340 m/s,what is the smallest size insect they can detect?

A wave travels in a string at 64 m/s.A second string of 25% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string?

An object is attached to a spring and its frequency of oscillation is measured.Then another object is connected to the first object,and the resulting mass is three times the original value.By what factor is the frequency of oscillation changed?

Suppose a 0.36-kg mass on a spring-loaded gun that has been compressed 0.2 m has elastic potential energy of 1.9 J.How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?

Exam 13: Vibrations and Waves

By what factor should the length of a simple pendulum be changed if the period of vibration were to be two times? ​

Transverse waves travel with a speed of 100 m/s along a taut copper wire that has a diameter of 1.73 mm.What is the tension in the wire? (The density of copper is 8.93 g/cm3. ) ​

For a mass suspended on a spring in the vertical direction,the time for one complete oscillation will depend on:

A 0.39 kg object,attached to a spring with spring constant k = 15 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.082 m.What is its speed at the instant when its displacement is 0.041 m? (Hint: Use conservation of energy. ) ​

A wave is traveling in a string at 68 m/s.When the tension is then increased 15%,what will be the resulting wave speed? ​

Two springs,each with spring constant 10 N/m,are connected in parallel,and the combination is hung vertically from one end.A 20-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium? ​

For a wave on the ocean,the amplitude is:

Spring #1 has spring constant 80 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective force constant of 10 N/m.What is the spring constant for Spring #2? ​

The motion of a piston in an automobile engine is nearly simple harmonic.If the 1-kg piston travels back and forth over a total distance of 11.9 cm,what is its maximum speed when the engine is running at 3,540 rpm? ​

An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth.A P-wave travels at 9,000 m/s and an S-wave at 4,000 m/s.If P-waves are received at a seismic station 44.2 s before an S-wave arrives,how far is the station from the earthquake center? ​

A car with bad shocks bounces up and down with a period of 1.62 s after hitting a bump.The car has a mass of 1,600 kg and is supported by four springs of force constant k.What is k for each spring? ​

What is the phase difference when two waves,traveling in the same medium,undergo constructive interference?

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.4 Hz and an amplitude of 8.6 cm.If the mass of the object is 0.4 kg,what is the spring constant? ​

Bats can detect small objects such as insects that are of a size approximately that of one wavelength.If bats emit a chirp at a frequency of 60 kHz,and the speed of sound waves in air is 340 m/s,what is the smallest size insect they can detect? ​

A wave travels in a string at 64 m/s.A second string of 25% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string? ​

An object is attached to a spring and its frequency of oscillation is measured.Then another object is connected to the first object,and the resulting mass is three times the original value.By what factor is the frequency of oscillation changed? ​

Suppose a 0.36-kg mass on a spring-loaded gun that has been compressed 0.2 m has elastic potential energy of 1.9 J.How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up? ​

By what factor should the length of a simple pendulum be changed if the period of vibration were to be two times?

Transverse waves travel with a speed of 100 m/s along a taut copper wire that has a diameter of 1.73 mm.What is the tension in the wire? (The density of copper is 8.93 g/cm³. )

A 0.39 kg object,attached to a spring with spring constant k = 15 N/m,is moving on a horizontal frictionless surface in simple harmonic motion of amplitude of 0.082 m.What is its speed at the instant when its displacement is 0.041 m? (Hint: Use conservation of energy. )

A wave is traveling in a string at 68 m/s.When the tension is then increased 15%,what will be the resulting wave speed?

Two springs,each with spring constant 10 N/m,are connected in parallel,and the combination is hung vertically from one end.A 20-N weight is then suspended from the other end of the combined spring.How far does the combined spring stretch as it comes to equilibrium?

Spring #1 has spring constant 80 N/m.Spring #2 has an unknown spring constant,but when connected in series with Spring #1,the connected springs have an effective force constant of 10 N/m.What is the spring constant for Spring #2?

The motion of a piston in an automobile engine is nearly simple harmonic.If the 1-kg piston travels back and forth over a total distance of 11.9 cm,what is its maximum speed when the engine is running at 3,540 rpm?

An earthquake emits both P-waves and S-waves that travel at different speeds through the Earth.A P-wave travels at 9,000 m/s and an S-wave at 4,000 m/s.If P-waves are received at a seismic station 44.2 s before an S-wave arrives,how far is the station from the earthquake center?

A car with bad shocks bounces up and down with a period of 1.62 s after hitting a bump.The car has a mass of 1,600 kg and is supported by four springs of force constant k.What is k for each spring?

A mass on a spring vibrates in simple harmonic motion at a frequency of 4.4 Hz and an amplitude of 8.6 cm.If the mass of the object is 0.4 kg,what is the spring constant?

Bats can detect small objects such as insects that are of a size approximately that of one wavelength.If bats emit a chirp at a frequency of 60 kHz,and the speed of sound waves in air is 340 m/s,what is the smallest size insect they can detect?

A wave travels in a string at 64 m/s.A second string of 25% greater linear density has the same tension applied as in the first string.What will be the resulting wave speed in the second string?

An object is attached to a spring and its frequency of oscillation is measured.Then another object is connected to the first object,and the resulting mass is three times the original value.By what factor is the frequency of oscillation changed?

Suppose a 0.36-kg mass on a spring-loaded gun that has been compressed 0.2 m has elastic potential energy of 1.9 J.How high above the spring's equilibrium point can the gun fire the mass if the gun is fired straight up?