Question 1

Suppose you wish to lower the pitch of a violin string by 2 octaves. This could be done by

Accepted Answer

To lower the pitch by 2 octaves, the frequency must be reduced by a factor of 4. Increasing the diameter quadruples the mass per unit length, reducing the frequency by a factor of 2 for each octave.

Question 2

What is the spring constant of a spring that stretches 2.0 cm when a mass of 0.60 kg is suspended from it?

Accepted Answer

The answer of What is the spring constant of a...

Question 3

A mountain climber of mass 60. kg slips and falls a distance of 4.0 m, at which time he reaches the end of his elastic safety rope. The rope then stretches an additional 2.0 m before the climber comes to rest. What is the spring constant of the rope, assuming it obeys Hooke's law?

Accepted Answer

The answer of A mountain climber of mass 60. kg...

Question 4

A spring-driven dart gun propels a 10. g dart. It is cocked by exerting a force of 20. N over a distance of 5.0 cm. With what speed will the dart leave the gun, assuming the spring has negligible mass?

Accepted Answer

The answer of A spring-driven dart gun propels a 10....

Question 5

A 0.30 kg mass is suspended on a string. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest.
(a) Calculate the period of oscillation. 
(b) Calculate the total energy of the system.

Accepted Answer

The answer of A 0.30 kg mass is suspended on...

Question 6

Tarzan swings back and forth on a long vine. His friend Jane notices 30. swings in 2.4 minutes.
(a) The frequency of the swing is ________.
(b) The vine length is ________ meters.

Accepted Answer

The answer of Tarzan swings back and forth on a...

Question 7

A 0.30 kg mass is suspended on a string. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest.
(a) Write down its equation of motion. 
(b) Calculate the velocity of the mass at T/3 s.

Accepted Answer

The answer of A 0.30 kg mass is suspended on...

Question 8

A simple pendulum has a length of 0.80 m and a bob of mass 0.20 kg. It is initially displaced to an angle of 18° from the vertical and released from rest. At t = 1.2 s:
(a) what angle does it make with the vertical?
(b) what is its velocity?

Accepted Answer

The answer of A simple pendulum has a length of...

Question 9

An object oscillates such that its displacement is x = (0.222 m) sin(314.t) where t is in seconds.
(a) In one period, the object moves what distance?
(b) What is the frequency?
(c) What is the position at t = 1.00 s?

Accepted Answer

The answer of An object oscillates such that its displacement...

Question 10

A spring has 0.770 kg oscillating on it with a period of 1.25 seconds.
(a) What is the frequency?
(b) Determine the spring constant.
(c) If the mass is doubled and the spring made 3 times stiffer, what is the new period?

Accepted Answer

The answer of A spring has 0.770 kg oscillating on...

Question 11

Suppose you want to set up a simple pendulum with a period of 0.250 s.
(a) What length is required if g = 9.80 m/sS1U1P12S1S1P0 on Earth?
(b) What length would be required on the moon assuming g is 6 (assume exact) times LESS than on Earth?

Accepted Answer

The answer of Suppose you want to set up a...

Question 12

The equation of motion of a particle undergoing simple harmonic motion is y = 2.0 sin(0.60t) where y is in cm. At t = 0.60 s determine the particle's:
(a) displacement.
(b) velocity.
(c) acceleration.

Accepted Answer

The answer of The equation of motion of a particle...

Question 13

A 1.33 kg dense mass is on the end of a 4.50 m "string".
(a) What would be the period of the pendulum on Earth?
(b) If the mass were doubled, what would be the frequency of oscillation?
(c) What would be the period on the planet Mars where gravity is 38.% that of the Earth?

Accepted Answer

The answer of A 1.33 kg dense mass is on...

Question 14

A string of linear density 6.00 g/m is under a tension of 180. N. What is the velocity of propagation of transverse waves along the string?

Accepted Answer

The answer of A string of linear density 6.00 g/m...

Question 15

A stretched string is observed to have three equal segments in a standing wave driven at a frequency of 480. Hz. What driving frequency will set up a standing wave with four equal segments?

Accepted Answer

The answer of A stretched string is observed to have...

Question 16

What are the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N?

Accepted Answer

The answer of What are the first three harmonics of...

Question 17

A string fixed at both ends is vibrating in its 8th harmonic.
(a) How many nodes are on the string?
(b) The 8th harmonic wavelength is what fraction of the string length?
(c) If the 8th harmonic frequency is 976. Hz, what is the frequency of the 2nd overtone?

Accepted Answer

The answer of A string fixed at both ends is...

Question 18

A long rope of linear density 0.25 kg/m is under tension. Transverse waves travel on it at 30. m/s. How much energy is stored in 1.0 m of the rope when a driving frequency of 6.0 Hz produces a traveling wave with an amplitude of 0.10 m?

Accepted Answer

The answer of A long rope of linear density 0.25...

Question 19

A string of length 2.5 m is fixed at both ends. When the string vibrates at a frequency of 85 Hz, a standing wave with five loops is formed.
(a) Determine the distance between two adjacent nodes.
(b) Determine the wavelength of the waves that travel on the string.
(c) Determine the velocity of waves.
(d) Determine the fundamental frequency of this string.

Accepted Answer

The answer of A string of length 2.5 m is...

Question 20

A 2.0 kg mass is attached to the end of a horizontal spring (k = 50. N/m) and set into simple harmonic motion with an amplitude of 10. cm. What is the total mechanical energy of this system?

Accepted Answer

The total mechanical energy in a spring-mass system is given by E = (1/2)kA^2. Substituting k = 50 N/m and A = 0.1 m, E = 0.25 J.

Quiz 13: Vibrations and Waves

Suppose you wish to lower the pitch of a violin string by 2 octaves. This could be done by

What is the spring constant of a spring that stretches 2.0 cm when a mass of 0.60 kg is suspended from it?

A mountain climber of mass 60. kg slips and falls a distance of 4.0 m, at which time he reaches the end of his elastic safety rope. The rope then stretches an additional 2.0 m before the climber comes to rest. What is the spring constant of the rope, assuming it obeys Hooke's law?

A spring-driven dart gun propels a 10. g dart. It is cocked by exerting a force of 20. N over a distance of 5.0 cm. With what speed will the dart leave the gun, assuming the spring has negligible mass?

A 0.30 kg mass is suspended on a string. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. (a) Calculate the period of oscillation. (b) Calculate the total energy of the system.

Tarzan swings back and forth on a long vine. His friend Jane notices 30. swings in 2.4 minutes. (a) The frequency of the swing is . (b) The vine length is meters.

A 0.30 kg mass is suspended on a string. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. (a) Write down its equation of motion. (b) Calculate the velocity of the mass at T/3 s.

A simple pendulum has a length of 0.80 m and a bob of mass 0.20 kg. It is initially displaced to an angle of 18° from the vertical and released from rest. At t = 1.2 s: (a) what angle does it make with the vertical? (b) what is its velocity?

An object oscillates such that its displacement is x = (0.222 m) sin(314.t) where t is in seconds. (a) In one period, the object moves what distance? (b) What is the frequency? (c) What is the position at t = 1.00 s?

A spring has 0.770 kg oscillating on it with a period of 1.25 seconds. (a) What is the frequency? (b) Determine the spring constant. (c) If the mass is doubled and the spring made 3 times stiffer, what is the new period?

Suppose you want to set up a simple pendulum with a period of 0.250 s. (a) What length is required if g = 9.80 m/s² on Earth? (b) What length would be required on the moon assuming g is 6 (assume exact) times LESS than on Earth?

The equation of motion of a particle undergoing simple harmonic motion is y = 2.0 sin(0.60t) where y is in cm. At t = 0.60 s determine the particle's: (a) displacement. (b) velocity. (c) acceleration.

A 1.33 kg dense mass is on the end of a 4.50 m "string". (a) What would be the period of the pendulum on Earth? (b) If the mass were doubled, what would be the frequency of oscillation? (c) What would be the period on the planet Mars where gravity is 38.% that of the Earth?

A string of linear density 6.00 g/m is under a tension of 180. N. What is the velocity of propagation of transverse waves along the string?

A stretched string is observed to have three equal segments in a standing wave driven at a frequency of 480. Hz. What driving frequency will set up a standing wave with four equal segments?

What are the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N?

A string fixed at both ends is vibrating in its 8th harmonic. (a) How many nodes are on the string? (b) The 8th harmonic wavelength is what fraction of the string length? (c) If the 8th harmonic frequency is 976. Hz, what is the frequency of the 2nd overtone?

A long rope of linear density 0.25 kg/m is under tension. Transverse waves travel on it at 30. m/s. How much energy is stored in 1.0 m of the rope when a driving frequency of 6.0 Hz produces a traveling wave with an amplitude of 0.10 m?

A 2.0 kg mass is attached to the end of a horizontal spring (k = 50. N/m) and set into simple harmonic motion with an amplitude of 10. cm. What is the total mechanical energy of this system?

Quiz 13: Vibrations and Waves

Suppose you wish to lower the pitch of a violin string by 2 octaves. This could be done by

What is the spring constant of a spring that stretches 2.0 cm when a mass of 0.60 kg is suspended from it?

A mountain climber of mass 60. kg slips and falls a distance of 4.0 m, at which time he reaches the end of his elastic safety rope. The rope then stretches an additional 2.0 m before the climber comes to rest. What is the spring constant of the rope, assuming it obeys Hooke's law?

A spring-driven dart gun propels a 10. g dart. It is cocked by exerting a force of 20. N over a distance of 5.0 cm. With what speed will the dart leave the gun, assuming the spring has negligible mass?

A 0.30 kg mass is suspended on a string. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. (a) Calculate the period of oscillation. (b) Calculate the total energy of the system.

Tarzan swings back and forth on a long vine. His friend Jane notices 30. swings in 2.4 minutes. (a) The frequency of the swing is ________. (b) The vine length is ________ meters.

A 0.30 kg mass is suspended on a string. In equilibrium the mass stretches the spring 2.0 cm downward. The mass is then pulled an additional distance of 1.0 cm down and released from rest. (a) Write down its equation of motion. (b) Calculate the velocity of the mass at T/3 s.

A simple pendulum has a length of 0.80 m and a bob of mass 0.20 kg. It is initially displaced to an angle of 18° from the vertical and released from rest. At t = 1.2 s: (a) what angle does it make with the vertical? (b) what is its velocity?

An object oscillates such that its displacement is x = (0.222 m) sin(314.t) where t is in seconds. (a) In one period, the object moves what distance? (b) What is the frequency? (c) What is the position at t = 1.00 s?

A spring has 0.770 kg oscillating on it with a period of 1.25 seconds. (a) What is the frequency? (b) Determine the spring constant. (c) If the mass is doubled and the spring made 3 times stiffer, what is the new period?

Suppose you want to set up a simple pendulum with a period of 0.250 s. (a) What length is required if g = 9.80 m/s2 on Earth? (b) What length would be required on the moon assuming g is 6 (assume exact) times LESS than on Earth?

The equation of motion of a particle undergoing simple harmonic motion is y = 2.0 sin(0.60t) where y is in cm. At t = 0.60 s determine the particle's: (a) displacement. (b) velocity. (c) acceleration.

A 1.33 kg dense mass is on the end of a 4.50 m "string". (a) What would be the period of the pendulum on Earth? (b) If the mass were doubled, what would be the frequency of oscillation? (c) What would be the period on the planet Mars where gravity is 38.% that of the Earth?

A string of linear density 6.00 g/m is under a tension of 180. N. What is the velocity of propagation of transverse waves along the string?

A stretched string is observed to have three equal segments in a standing wave driven at a frequency of 480. Hz. What driving frequency will set up a standing wave with four equal segments?

What are the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N?

A string fixed at both ends is vibrating in its 8th harmonic. (a) How many nodes are on the string? (b) The 8th harmonic wavelength is what fraction of the string length? (c) If the 8th harmonic frequency is 976. Hz, what is the frequency of the 2nd overtone?

A long rope of linear density 0.25 kg/m is under tension. Transverse waves travel on it at 30. m/s. How much energy is stored in 1.0 m of the rope when a driving frequency of 6.0 Hz produces a traveling wave with an amplitude of 0.10 m?

A 2.0 kg mass is attached to the end of a horizontal spring (k = 50. N/m) and set into simple harmonic motion with an amplitude of 10. cm. What is the total mechanical energy of this system?

Tarzan swings back and forth on a long vine. His friend Jane notices 30. swings in 2.4 minutes. (a) The frequency of the swing is . (b) The vine length is meters.

Suppose you want to set up a simple pendulum with a period of 0.250 s. (a) What length is required if g = 9.80 m/s² on Earth? (b) What length would be required on the moon assuming g is 6 (assume exact) times LESS than on Earth?