Marine Institute of Memorial University of Newfoundland



Physics: Principle and Applications, 7e (Giancoli)

Chapter 11 Oscillation and Waves

11.1 Conceptual Questions

1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one correct choice.)

A) The period is doubled.

B) The angular frequency is doubled.

C) The amplitude is doubled.

D) The period is reduced to one-half of what it was.

E) The angular frequency is reduced to one-half of what it was.

Answer: B, D

Var: 1

2) A simple harmonic oscillator oscillates with frequency f when its amplitude is A. If the amplitude is now doubled to 2A, what is the new frequency?

A) 2f

B) 4f

C) f

D) f/2

E) f/4

Answer: C

Var: 1

3) The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the velocity of this system as a function of time?

[pic]

[pic]

A) graph a

B) graph b

C) graph c

D) graph d

Answer: B

Var: 1

4) The figure shows a graph of the velocity v as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time?

[pic]

[pic]

A) graph a

B) graph b

C) graph c

D) graph d

Answer: B

Var: 1

5) The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion. Which one of the following graphs represents the acceleration of this system as a function of time?

[pic]

[pic]

A) graph a

B) graph b

C) graph c

D) graph d

Answer: A

Var: 1

6) In simple harmonic motion, when is the speed the greatest? (There could be more than one correct choice.)

A) when the magnitude of the acceleration is a maximum

B) when the displacement is a maximum

C) when the magnitude of the acceleration is a minimum

D) when the potential energy is a maximum

E) when the potential energy is a zero

Answer: C, E

Var: 1

7) In simple harmonic motion, when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.)

A) when the speed is a maximum

B) when the displacement is a zero

C) when the magnitude of the displacement is a maximum

D) when the potential energy is a maximum

E) when the kinetic energy is a minimum

Answer: C, D, E

Var: 1

8) The total mechanical energy of a simple harmonic oscillating system is

A) zero as it passes the equilibrium point.

B) zero when it reaches the maximum displacement.

C) a maximum when it passes through the equilibrium point.

D) a minimum when it passes through the equilibrium point.

E) a non-zero constant.

Answer: E

Var: 1

9) An object attached to an ideal spring executes simple harmonic motion. If you want to double its total energy, you could

A) double the amplitude of vibration.

B) double the force constant (spring constant) of the spring.

C) double both the amplitude and force constant (spring constant).

D) double the mass.

E) double both the mass and amplitude of vibration.

Answer: B

Var: 1

10) An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T. If the elevator accelerates upward with acceleration 2g, what will be the period of oscillation of the object?

A) 4T

B) 2T

C) T

D) T/2

E) T/4

Answer: C

Var: 1

11) A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.)

A) Its acceleration is zero.

B) Its speed is zero.

C) Its elastic potential energy is zero.

D) Its kinetic energy is a maximum.

E) Its total mechanical energy is zero.

Answer: A, C, D

Var: 1

12) A mass on a spring undergoes SHM. When the mass is at its maximum distance from the equilibrium position, which of the following statements about it are true? (There could be more than one correct choice.)

A) Its acceleration is zero.

B) Its speed is zero.

C) Its elastic potential energy is zero.

D) Its kinetic energy is a maximum.

E) Its total mechanical energy is zero.

Answer: B

Var: 1

13) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a minimum?

A) at either A or B

B) midway between A and B

C) one-third of the way between A and B

D) one-fourth of the way between A and B

E) at none of the above points

Answer: A

Var: 1

14) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its kinetic energy is a maximum?

A) at either A or B

B) midway between A and B

C) one-third of the way between A and B

D) one-fourth of the way between A and B

E) at none of the above points

Answer: B

Var: 1

15) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a minimum?

A) at either A or B

B) midway between A and B

C) one-third of the way between A and B

D) one-fourth of the way between A and B

E) at none of the above points

Answer: B

Var: 1

16) An object is attached to a vertical spring and bobs up and down between points A and B. Where is the object located when its elastic potential energy is a maximum?

A) at either A or B

B) midway between A and B

C) one-third of the way between A and B

D) one-fourth of the way between A and B

E) at none of the above points

Answer: A

Var: 1

17) Two simple pendulums, A and B, are each 3.0 m long, and the period of pendulum A is T. Pendulum A is twice as heavy as pendulum B. What is the period of pendulum B?

A) T/[pic]

B) T

C) T[pic]

D) 2T

E) T/2

Answer: B

Var: 1

18) A ball swinging at the end of a massless string, as shown in the figure, undergoes simple harmonic motion. At what point (or points) is the magnitude of the instantaneous acceleration of the ball the greatest?

[pic]

A) C

B) A and D

C) A and C

D) A and B

E) B

Answer: B

Var: 1

19) Identical balls oscillate with the same period T on Earth. Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum. These systems are now taken to the Moon, where g = 1.6 m/s2, and set into oscillation. Which of the following statements about these systems are true? (There could be more than one correct choice.)

A) Both systems will have the same period on the Moon as on Earth.

B) On the Moon, ball A will take longer to complete one cycle than ball B.

C) On the Moon, ball B will take longer to complete one cycle than ball A.

D) On the Moon, ball A will execute more vibrations each minute than ball B.

E) On the Moon, ball B will execute more vibrations each minute than ball A.

Answer: C, D

Var: 1

20) Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs slow. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.)

A) Raise the weight.

B) Lower the weight.

C) Add more mass to the weight.

D) Remove some mass from the weight.

E) Increase the amplitude of swing by a small amount.

Answer: A

Var: 1

21) Grandfather clocks are designed so they can be adjusted by moving the weight at the bottom of the pendulum up or down. Suppose you have a grandfather clock at home that runs fast. Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice.)

A) Raise the weight.

B) Lower the weight.

C) Add more mass to the weight.

D) Remove some mass from the weight.

E) Decrease the amplitude of swing by a small amount.

Answer: B

Var: 1

22) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant acceleration?

A) The period does not change.

B) The period increases.

C) The period decreases.

D) The period becomes zero.

E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Answer: C

Var: 1

23) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration?

A) The period does not change.

B) The period increases.

C) The period decreases.

D) The period becomes zero.

E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Answer: B

Var: 1

24) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves upward with constant velocity?

A) The period does not change.

B) The period increases.

C) The period decreases.

D) The period becomes zero.

E) The period increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Answer: A

Var: 1

25) A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How would the period of the pendulum change if the supporting chain were to break, putting the elevator into freefall?

A) The period does not change.

B) The period increases slightly.

C) The period decreases slightly.

D) The period becomes zero.

E) The period becomes infinite because the pendulum would not swing.

Answer: E

Var: 1

26) A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now accelerates downward uniformly at 2 m/s2, what is true about the periods of these two systems?

A) Both periods would remain the same.

B) Both periods would increase.

C) Both periods would decrease.

D) The period of the pendulum would increase but the period of the spring would stay the same.

E) The period of the pendulum would decrease but the period of the spring would stay the same.

Answer: D

Var: 1

27) A simple pendulum and a mass oscillating on an ideal spring both have period T in an elevator at rest. If the elevator now moves downward at a uniform 2 m/s, what is true about the periods of these two systems?

A) Both periods would remain the same.

B) Both periods would increase.

C) Both periods would decrease.

D) The period of the pendulum would increase but the period of the spring would stay the same.

E) The period of the pendulum would decrease but the period of the spring would stay the same.

Answer: A

Var: 1

28) What is the wavelength of the wave shown in the figure?

[pic]

A) 8 m.

B) 4 m.

C) 2 m.

D) 1 m.

E) It cannot be determined from the given information.

Answer: E

Var: 1

29) What is the frequency of the wave shown in the figure?

[pic]

A) 0.5 Hz.

B) 1 Hz.

C) 2 Hz.

D) 4 Hz.

E) It cannot be determined from the given information.

Answer: A

Var: 1

30) Which one of the curves shown in the figure best represents the variation of wave speed v as a function of tension for transverse waves on a stretched string?

[pic]

A) A

B) B

C) C

D) D

E) E

Answer: B

Var: 1

31) A string of mass m is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension?

A) v/2

B) v/[pic]

C) v[pic]

D) 2v

E) 4v

Answer: B

Var: 1

32) A string of length L is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L but with no change in the mass or tension?

A) v/2

B) v/[pic]

C) v[pic]

D) 2v

E) 4v

Answer: C

Var: 1

33) When a certain string is under tension T, the speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string?

A) v/2

B) v/[pic]

C) v[pic]

D) 2v

E) 4v

Answer: C

Var: 1

34) Four waves are described by the following equations, where distances are measured in meters and times in seconds.

I. y = 0.12 cos(3x - 21t)

II. y = 0.15 sin(6x + 42t)

III. y = 0.13 cos(6x + 21t)

IV. y = -0.23 sin(3x - 42t)

Which of these waves have the same speed?

A) I and II

B) I and III

C) II and III

D) III and IV

E) II and IV

Answer: A

Var: 1

35) Four waves are described by the following equations, where distances are measured in meters and times in seconds.

I. y = 0.12 cos(3x - 21t)

II. y = 0.15 sin(6x + 42t)

III. y = 0.13 cos(6x + 21t)

IV. y = -0.23 sin(3x - 42t)

Which of these waves have the same period?

A) I and III, and also II and IV

B) I and IV, and also II and III

C) I and II, and also III and IV

D) All of them have the same period.

E) They all have different periods.

Answer: A

Var: 1

36) The intensity of the waves from a point source at a distance d from the source is I. What is the intensity at a distance 2d from the source?

A) 4I

B) 2I

C) I/2

D) I/4

E) I/[pic]

Answer: D

Var: 1

37) The intensity of the waves from a point source at a distance d from the source is I. At what distance from the sources is the intensity equal to 2I?

A) d/2

B) d/[pic]

C) d/4

D) d/8

Answer: B

Var: 1

38) Why does the intensity of waves from a small source decrease with the square of the distance from the source?

A) The waves run out of energy as they travel.

B) The waves spread out as they travel.

C) The medium through which the waves travel absorbs the energy of the waves.

D) The waves slow down as they travel away from the source.

E) The frequency of the waves decreases as they get farther from the source.

Answer: B

Var: 1

39) When a guitar is tuned to adjust it pitch, what is it that is changed?

A) The wavelength of the fundamental.

B) The frequency of the fundamental.

C) The amplitude of the fundamental.

Answer: B

Var: 1

40) If a guitar string has a fundamental frequency of 500 Hz, which one of the following frequencies can set the string into resonant vibration?

A) 250 Hz

B) 750 Hz

C) 1500 Hz

D) 1750 Hz

Answer: C

Var: 1

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

A) 600 Hz

B) 360 Hz

C) 240 Hz

D) 120 Hz

Answer: A

Var: 1

42) If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz, at which of the following frequencies will it not resonate? (There could be more than one correct choice.)

A) 75 Hz

B) 300 Hz

C) 450 Hz

D) 500 Hz

E) 600 Hz

Answer: A, D

Var: 1

43) A string fixed at both ends is vibrating in one of its harmonics. If we now increase only the frequency at which the string is vibrating, which of the following characteristics do we also increase? (There could be more than one correct choice.)

A) the speed of the traveling waves on the string

B) the period of the traveling waves on the string

C) the wavelength of the traveling waves on the string

D) the amplitude of the traveling waves on the string

E) none of the above

Answer: E

Var: 1

11.2 Problems

1) A leaky faucet drips 40 times in [pic] What is the frequency of the dripping?

A) 1.3 Hz

B) 0.75 Hz

C) 1.6 Hz

D) 0.63 Hz

Answer: A

Var: 21

2) An object is undergoing simple harmonic motion of amplitude 2.3 m. If the maximum velocity of the object is 10 m/s, what is the object's angular frequency?

A) 4.3 rad/s

B) 4.8 rad/s

C) 3.5 rad/s

D) 4.0 rad/s

Answer: A

Var: 1

3) If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you, what are the frequency and period of the wave?

Answer: 0.25 Hz, 4.0 s

Var: 1

4) The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?

A) 30.5 µs

B) 15.3 µs

C) 95.8 µs

D) 0.191 ms

E) 9.71 µs

Answer: A

Var: 1

5) If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations in hertz?

A) 4560 Hz

B) 1450 Hz

C) 3.98 Hz

D) 2.54 Hz

E) 1.27 Hz

Answer: E

Var: 1

6) A guitar string is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo each minute?

A) 30,700

B) 8.53

C) 26.8

D) 1610

E) 512

Answer: A

Var: 1

7) A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. What are the (a) maximum speed and (b) maximum acceleration of the tip of the needle?

Answer: (a) 20.3 cm/s (b) 326 cm/s2

Var: 1

8) A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm.

(a) How long does it take the tip of the needle to move from the highest point to the lowest point in its travel?

(b) How long does it take the needle tip to travel a total distance of 11.43 cm?

Answer: (a) 0.20 s (b) 0.90 s

Var: 1

9) If the frequency of a system undergoing simple harmonic motion doubles, by what factor does the maximum value of acceleration change?

A) 4

B) 2

C) [pic]

D) 2/π

Answer: A

Var: 1

10) If a pendulum makes 12 complete swings in 8.0 s, what are its (a) frequency and (b) period?

Answer: (a) 1.5 Hz (b) 0.67 s

Var: 1

11) A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz.

(a) What is the maximum speed of that point in SI units?

(b) What is the maximum acceleration of the point in SI units?

Answer: (a) 6.82 m/s (b) 3.75 × 104 m/s2

Var: 1

12) The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm) cos[(1.26 s-1)t]. When t = 0.805 s, what are the (a) velocity and (b) acceleration of the cart?

Answer: (a) -13.2 cm/s (b) -10.3 cm/s2

Var: 1

13) The position of an object that is oscillating on a spring is given by the equation x = (18.3 cm) cos[(2.35 s-1)t]. What are the (a) frequency, (b) amplitude, and (c) period of this motion?

Answer: (a) 0.374 Hz (b) 18.3 cm (c) 2.67 s

Var: 1

14) The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm) cos[(6.35 s-1)t]. At what value of t after t = 0.00 s is the cart first located at x = 8.47 cm?

A) 4.34 s

B) 0.108 s

C) 0.129 s

D) 7.39 s

E) 7.75 s

Answer: C

Var: 1

15) An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion. At time t = 0.00 s the cart is released at the position x = +0.250 m. What is the position of the cart when t = 29.6 s?

A) x = 0.0461 m

B) x = 0.210 m

C) x = 0.218 m

D) x = 0.342 m

E) x = -0.218 m

Answer: A

Var: 1

16) The position of an object that is oscillating on a spring is given by the equation x = (17.4 cm) cos[(5.46 s-1)t]. What is the angular frequency for this motion?

A) 0.183 rad/s

B) 5.46 rad/s

C) 2.34 rad/s

D) 17.4 rad/s

E) 0.869 rad/s

Answer: B

Var: 1

17) An object is oscillating on a spring with a period of 4.60 s. At time t = 0.00 s the object has zero speed and is at x = 8.30 cm. What is the acceleration of the object at t = 2.50 s?

A) 1.33 cm/s2

B) 0.784 cm/s2

C) 11.5 cm/s2

D) 14.9 cm/s2

E) 0.00 cm/s2

Answer: D

Var: 1

18) A package is oscillating on a spring scale with a period of 4.60 s. At time t = 0.00 s the package has zero speed and is at x = 8.30 cm. At what time after t = 0.00 s will the package first be at x = 4.15 cm?

A) 0.575 s

B) 0.767 s

C) 1.15 s

D) 1.30 s

E) 1.53 s

Answer: B

Var: 1

19) A ball is oscillating on an ideal spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time t, if x is equal to 8.3 cm at t = 0.0 s. Use the cosine function.

Answer: x = (8.3 cm) cos[2πt/(4.6 s)] or x = (8.3 cm) cos[(1.4 s-1)t]

Var: 1

20) The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. Write an expression for the velocity of the particle as a function of time using the sine function.

Answer: v = - (95.0 cm/s) sin[(5.46 s-1)t]

Var: 1

21) The position of an object that is oscillating on an ideal spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. Write an expression for the acceleration of the particle as a function of time using the cosine function.

Answer: a = - (519 cm/s2) cos[(5.46 s-1)t]

Var: 1

22) An object oscillates such that its position x as a function of time t obeys the equation x = (0.222 m) sin(314 s-1 t), where t is in seconds.

(a) In one period, what total distance does the object move?

(b) What is the frequency of the motion?

(c) What is the position of the object when t = 1.00 s?

Answer: (a) 0.888 m (b) 50.0 Hz (c) -0.0352 m

Var: 1

23) An object undergoing simple harmonic motion has a maximum displacement of [pic] at [pic] If the angular frequency of oscillation is [pic] what is the object's displacement when [pic]

A) 4.8 m

B) 5.6 m

C) 3.7 m

D) 3.1 m

Answer: A

Var: 50+

24) If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

A) 2

B) 4

C) It does not change.

D) 1/2

E) 1/4

Answer: A

Var: 1

25) If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

A) 2

B) 4

C) It does not change.

D) 1/2

E) 1/4

Answer: A

Var: 1

26) If the angular frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change?

A) 2

B) 4

C) It does not change.

D) 1/2

E) 1/4

Answer: B

Var: 1

27) The equation of motion of a particle undergoing simple harmonic motion in the y direction is y = (2.0 cm) sin(0.60 s-1 t). At time t = 0.60 s determine the particle's (a) position, (b) velocity, and (c) acceleration.

Answer: (a) 0.70 cm (b) 1.1 cm/s (c) -0.25 cm/s2

Var: 1

28) A 0.25 kg harmonic oscillator has a total mechanical energy of [pic] If the oscillation amplitude is [pic] what is the oscillation frequency?

A) 4.6 Hz

B) 1.4 Hz

C) 2.3 Hz

D) 3.2 Hz

Answer: A

Var: 50+

29) A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant (spring constant) of the spring?

A) 2.45 N/m

B) 12.1 N/m

C) 24.1 N/m

D) 0.102 N/m

E) 0.610 N/m

Answer: C

Var: 1

30) A 0.150-kg air track cart is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations?

A) 2.57 s

B) 0.527 s

C) 0.263 s

D) 1.14 s

E) 1.29 s

Answer: E

Var: 1

31) In a supermarket, you place a 22.3-N (around 5 lb) bag of oranges on a scale, and the scale starts to oscillate at 2.7 Hz. What is the force constant (spring constant) of the spring of the scale?

A) 650 N/m

B) 600 N/m

C) 330 N/m

D) 820 N/m

E) 410 N/m

Answer: A

Var: 1

32) When a 0.350-kg package is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released. What is the period of the oscillations?

A) 0.695 s

B) 0.483 s

C) 0.286 s

D) 0.0769 s

E) 1.44 s

Answer: A

Var: 1

33) A 1.15-kg beaker (including its contents) is placed on a vertical spring scale. When the system is sent into vertical vibrations, it obeys the equation y = (2.3 cm)cos(17.4 s-1 t). What is the force constant (spring constant) of the spring scale, assuming it to be ideal?

Answer: 348 N/m

Var: 1

34) When a laboratory sample of unknown mass is placed on a vertical spring-scale having a force constant (spring constant) of 467 N/m, the system obeys the equation y = (4.4 cm) cos(33.3 s-1 t). What is the mass of this laboratory sample?

Answer: 0.421 kg

Var: 1

35) A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s2. If the force constant (spring constant) of the spring is [pic] find the period of oscillation of this setup on a planet where g = 1.60 m/s2.

A) 3.35 s

B) 2.51 s

C) 4.36 s

D) 5.70 s

Answer: A

Var: 31

36) A 51.8-kg bungee jumper jumps off a bridge and undergoes simple harmonic motion. If the period of oscillation is 11.2 s, what is the spring constant (force constant) of the bungee cord?

A) 16.3 N/m

B) 19.6 N/m

C) 26.1 N/m

Answer: A

Var: 50+

37) A 4.8-kg block attached to an ideal spring executes simple harmonic motion on a frictionless horizontal surface. At time t = 0.00 s, the block has a displacement of [pic] a velocity of [pic] and an acceleration of [pic] The force constant (spring constant) of the spring is closest to

A) 15 N/m.

B) 14 N/m.

C) 13 N/m.

D) 12 N/m.

E) 11 N/m.

Answer: A

Var: 50+

38) An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field. The spring stretches [pic] before it reaches its equilibrium position. If it were now allowed to oscillate by this spring, what would be its frequency?

A) 3.4 Hz

B) 0.28 x 10-3 Hz

C) 0.52 Hz

D) 1.6 Hz

Answer: A

Var: 50+

39) A 2.0-kg block on a frictionless table is connected to two springs whose opposite ends are fixed to walls, as shown in the figure. The springs have force constants (spring constants) k1 and k2. What is the oscillation angular frequency of the block if [pic] and [pic]

[pic]

A) 2.5 rad/s

B) 3.5 rad/s

C) 0.40 rad/s

D) 0.56 rad/s

Answer: A

Var: 50+

40) A 92-kg man climbs into a car with worn out shock absorbers, and this causes the car to drop down 4.5 cm. As he drives along he hits a bump, which starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car?

A) 890 kg

B) 760 kg

C) 920 kg

D) 990 kg

E) 1900 kg

Answer: A

Var: 1

41) An object attached to an ideal spring oscillates with an angular frequency of 2.81 rad/s. The object has a maximum displacement at t = 0.00 s of 0.232 m. If the force constant (spring constant) is [pic] what is the potential energy stored in the mass-spring system when t = 1.42 s?

A) 0.350 J

B) 0.256 J

C) 0.329 J

D) 0.399 J

Answer: A

Var: 50+

42) A block attached to an ideal spring of force constant (spring constant) 15 N/m executes simple harmonic motion on a frictionless horizontal surface. At time t = 0 s, the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s2 . The mass of the block is closest to

A) 2.3 kg

B) 2.6 kg

C) 4.7 kg

D) 9.4 kg

Answer: C

Var: 1

43) A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is [pic] The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position of the block is [pic] its kinetic energy is closest to

A) 0.90 J.

B) 0.84 J.

C) 0.95 J.

D) 1.0 J.

E) 1.1 J.

Answer: A

Var: 50+

44) A 0.16-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is 360 N/m. The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. When the position is x = -0.037 m, what is the acceleration of the block?

A) 83 m/s2

B) 43 m/s2

C) 64 m/s2

D) 270 m/s2

E) 370 m/s2

Answer: A

Var: 1

45) A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant) is [pic] The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest. The block then executes simple harmonic motion along the horizontal x-axis. The maximum elastic potential energy of the system is closest to

A) 1.4 J.

B) 1.3 J.

C) 1.6 J.

D) 1.7 J.

E) 1.8 J.

Answer: A

Var: 50+

46) An object of mass 6.8 kg is attached to an ideal spring of force constant (spring constant) 1720 N/m. The object is set into simple harmonic motion, with an initial velocity of [pic] and an initial displacement of [pic] Calculate the maximum speed the object raches during its motion.

Answer: 4.5 m/s

Var: 50+

47) A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg box. The larger box is attached to an ideal spring of force constant (spring constant) 150 N/m, as shown in the figure. Find (a) the amplitude of the resulting oscillations of this system, (b) the frequency of the oscillations and (c) the period of the oscillations.

[pic]

Answer: (a) 0.29 m, (b) 0.69 Hz, (c) 1.5 s

Var: 1

48) A ball is attached to an ideal spring and oscillates with a period T. If the mass of the ball is doubled, what is the new period?

A) 2T

B) T/2

C) T

D) T[pic]

E) T/[pic]

Answer: D

Var: 1

49) A geologist suspends a 0.30-kg stone on an ideal spring. In equilibrium the stone stretches the spring 2.0 cm downward. The stone is then pulled an additional distance of 1.0 cm down and released from rest.

(a) Write down the equation for the vertical position y of the stone as a function of time t, using the cosine function. Take the origin at the equilibrium point of the stone, with the positive y direction upward.

(b) How fast is the stone moving at a time equal to 1/3 of its period of motion?

Answer: (a) y = -(0.010 m) cos(22 s-1 t) (b) 0.19 m/s

Var: 1

50) How much mass should be attached to a vertical ideal spring having a spring constant (force constant) of 39.5 N/m so that it will oscillate at 1.00 Hz?

A) 39.5 kg

B) 2.00 kg

C) 1.00 kg

D) 1.56 kg

E) 6.29 kg

Answer: C

Var: 1

51) A 0.50-kg box is attached to an ideal spring of force constant (spring constant) 20 N/m on a horizontal, frictionless floor. The box oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position.

(a) What is the amplitude of vibration?

(b) At what distance from the equilibrium position are the kinetic energy and the potential energy the same?

Answer: (a) 0.24 m (b) 0.17 m

Var: 1

52) A 1.5-kg cart attached to an ideal spring with a force constant (spring constant) of 20 N/m oscillates on a horizontal, frictionless track. At time t = 0.00 s, the cart is released from rest at position x = 10 cm from the equilibrium position.

(a) What is the frequency of the oscillations of the cart?

(b) Determine the maximum speed of the cart. Where does the maximum speed occur?

(c) Find the maximum acceleration of the mass. Where does the maximum acceleration occur?

(d) How much total energy does this oscillating system contain?

(e) Express the displacement as a function of time using a cosine function.

Answer: (a) 0.58 Hz (b) 0.37 m/s, at the equilibrium position

(c) 1.3 m/s2, at maximum displacement (d) 0.10 J (e) x = (0.10 m) cos (3.7 s-1 t)

Var: 1

53) A 0.150-kg cart that is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m undergoes simple harmonic oscillations with an amplitude of 7.50 cm. What is the total mechanical energy of the system?

A) 0.0201 J

B) 0.0101 J

C) 0.269 J

D) 0.134 J

E) 0 J

Answer: B

Var: 1

54) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. What are (a) the total energy and (b) the amplitude of vibration of the system?

Answer: (a) 0.56 J (b) 0.24 m

Var: 1

55) A 0.50-kg object is attached to an ideal spring of spring constant (force constant) 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. At what distance from the equilibrium position are the kinetic energy and potential energy of the system the same?

A) 0.017 m

B) 0.029 m

C) 0.12 m

D) 0.17 m

Answer: D

Var: 1

56) A 1.53-kg piece of iron is hung by a vertical ideal spring. When perturbed slightly, the system is moves up and down in simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. If we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging iron, what is the total mechanical energy of the system?

A) 0.844 J

B) 0.646 J

C) 0.633 J

D) 0.955 J

E) 0.000 J

Answer: B

Var: 1

57) A 0.30-kg block of wood is suspended on a spring. In equilibrium the wood stretches the spring 2.0 cm downward. The wood is then pulled an additional distance of 1.0 cm down and released from rest.

(a) How long does it take the wood to make 3 complete cycles of vibration?

(b) How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational) to be zero at the equilibrium position of the hanging block?

Answer: (a) 0.84 s (b) 7.4 mJ

Var: 1

58) A ball vibrates back and forth from the free end of an ideal spring having a force constant (spring constant) of 20 N/m. If the amplitude of this motion is 0.30 m, what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position?

A) 0.00 J

B) 0.22 J

C) 0.45 J

D) 0.90 J

E) 1.4 J

Answer: A

Var: 1

59) What is the length of a simple pendulum with a period of 2.0 s?

A) 20 m

B) 0.99 m

C) 1.2 m

D) 1.6 m

E) 0.87 m

Answer: B

Var: 1

60) A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is [pic] how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables.

A) 4.4 s

B) 4.8 s

C) 5.3 s

D) 5.7 s

Answer: A

Var: 30

61) The period of a simple pendulum that is 1.00 m long on another planet is [pic] What is the acceleration due to gravity on this planet if the mass of the pendulum bob is 1.5 kg?

A) 14.3 m/s2

B) 13.3 m/s2

C) 15.7 m/s2

D) 17.2 m/s2

Answer: A

Var: 50+

62) On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon?

A) T[pic]

B) T/[pic]

C) T/6

D) 6T

E) T/3

Answer: A

Var: 1

63) A simple pendulum has a period T on Earth. If it were used on Planet X, where the acceleration due to gravity is 3 times what it is on Earth, what would its period be?

A) 3T

B) [pic]T

C) T

D) T/[pic]

E) T/3

Answer: D

Var: 1

64) A simple pendulum having a bob of mass M has a period T. If you double M but change nothing else, what would be the new period?

A) 2T

B) T[pic]

C) T

D) T/[pic]

E) T/2

Answer: C

Var: 1

65) If both the mass of a simple pendulum and its length are doubled, the period will

A) be unchanged.

B) increase by a factor of 2.

C) increase by a factor of 4.

D) increase by a factor of [pic].

E) increase by a factor of 1/[pic].

Answer: D

Var: 1

66) A simple pendulum takes 2.00 s to make one compete swing. If we now triple the length, how long will it take for one complete swing?

A) 6.00 s

B) 3.46 s

C) 2.00 s

D) 1.15 s

E) 0.667 s

Answer: B

Var: 1

67) Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes.

(a) What is the frequency (in hertz) of Tarzan's swing?

(b) How long is the vine he is using?

Answer: (a) 0.21 Hz (b) 5.7 m

Var: 1

68) As shown in the figure, a 0.23-kg ball is suspended from a string 6.87 m long and is pulled slightly to the left. As the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant (force constant) is [pic] (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

[pic]

Answer: 3.0 s

Var: 50+

69) When a certain simple pendulum is set swinging, its angular displacement θ as a function of time t obeys the equation θ = 8.5° cos(2.4 s-1t). How long is the pendulum?

Answer: 1.7 m

Var: 1

70) A spaceship captain lands on an unknown planet. Before venturing forth, he needs to find out the acceleration due to gravity on that planet. All he has available to him is some thin light string, a stopwatch, and a small 2.75-kg metal ball (it was a rough landing). So he lets the ball swing from a 1.5-m length of the string, starting at rest, and measures that it takes 1.9 s for it to swing from the place where he released it to the place where it first stops as it reverses direction. What is the acceleration due to gravity on this planet?

Answer: 4.1 m/s2

Var: 1

71) An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that planet. She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0 s. What is the acceleration of gravity on Planet N-40?

A) 4.85 m/s2

B) 1.66 m/s2

C) 3.74 m/s2

D) 2.39 m/s2

E) 9.81 m/s2

Answer: C

Var: 1

72) An astronaut has landed on an asteroid and conducts an experiment to determine the acceleration of gravity on that asteroid. He uses a simple pendulum that has a period of oscillation of 2.00 s on Earth and finds that on the asteroid the period is 11.3 s. What is the acceleration of gravity on that asteroid?

A) 0.307 m/s2

B) 1.66 m/s2

C) 1.74 m/s2

D) 5.51 m/s2

E) 0.0544 m/s2

Answer: A

Var: 1

73) In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. How long would it have taken for Foucault's pendulum to make one complete swing back to its starting point if g = 9.81 m/s2 at the observatory?

A) 6.65 s

B) 5.63 s

C) 1.79 s

D) 2.12 s

E) 2.58 s

Answer: A

Var: 1

74) A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0-kg sphere suspended from a 67.0-m light cable. How long would it take for the bob in this pendulum to move from the position of maximum displacement down to the equilibrium point?

A) 4.11 s

B) 21.5 s

C) 2.58 s

D) 32.2 s

E) 42.9 s

Answer: A

Var: 1

75) Suppose you want to set up a simple pendulum with a period of 2.50 s. How long should it be

(a) on Earth, at a location where g = 9.80 m/s2?

(b) on a planet where g is 5.00 times what it is on Earth?

Answer: (a) 1.55 m (b) 7.76 m

Var: 1

76) A fisherman fishing from a pier observes that the float on his line bobs up and down, taking 2.4 s to move from its highest point to its lowest point. He also estimates that the distance between adjacent wave crests is 48 m. What is the speed of the waves going past the pier?

A) 1.0 m/s

B) 20 m/s

C) 10 m/s

D) 5.0 m/s

E) 120 m/s

Answer: C

Var: 1

77) A tsunami, an ocean wave generated by an earthquake, propagates along the open ocean at 700 km/hr and has a wavelength of 750 km. What is the frequency of the waves in such a tsunami?

A) 0.93 Hz

B) 0.00026 Hz

C) 1.1 Hz

D) 6.8 Hz

E) 0.15 Hz

Answer: B

Var: 1

78) What is the frequency of a pressure wave of wavelength 2.5 m that is traveling at 1400 m/s?

A) 178 Hz

B) 1.78 kHz

C) 560 Hz

D) 5.6 kHz

Answer: C

Var: 1

79) If a wave has a speed of 362 m/s and a period of 4.17 ms, what is its wavelength?

A) 1510 m

B) 1.51 m

C) 86.8 m

D) 86,800 m

E) 0.0115 m

Answer: B

Var: 1

80) The figure shows a "snapshot" of a wave at a given instant of time. The frequency of this wave is 120 Hz. What are the (a) amplitude, (b) wavelength, and (c) speed of this wave?

[pic]

Answer: (a) 0.10 m (b) 0.20 m (c) 24 m/s

Var: 1

81) The speed of sound in steel is 5000 m/s. What is the wavelength of a sound wave of frequency [pic] in steel?

A) 7.58 m

B) 2.41 m

C) 1.21 m

D) 0.829 m

E) 0.132 m

Answer: A

Var: 50+

82) Crests of an ocean wave pass a pier every [pic] If the waves are moving at [pic] what is the wavelength of the ocean waves?

A) 56 m

B) 28 m

C) 64 m

D) 48 m

Answer: A

Var: 8

83) Transverse waves travel at [pic] in a string that is subjected to a tension of [pic] If the string is [pic] long, what is its mass?

A) 0.515 kg

B) 0.216 kg

C) 0.366 kg

D) 0.597 kg

Answer: A

Var: 50+

84) A piano wire of linear mass density 0.0050 kg/m is under a tension of 1350 N. What is the wave speed in this wire?

A) 130 m/s

B) 260 m/s

C) 520 m/s

D) 1040 m/s

Answer: C

Var: 1

85) A wave whose wavelength is 0.500 m is traveling down a 500-m long wire whose total mass is 25 kg and is under a tension of 2000 N.

(a) What is the speed of the wave on the wire?

(b) Find the frequency of this wave.

Answer: (a) 200 m/s (b) 400 Hz

Var: 1

86) The density of aluminum is 2700 kg/m3. If transverse waves travel at [pic] in an aluminum wire of diameter [pic] what is the tension on the wire?

A) 65 N

B) 39 N

C) 52 N

D) 78 N

Answer: A

Var: 21

87) A rope with a total mass of 25.0 kg is tied to a tree on one side of a 125-m wide ravine. You are pulling on the other end of the rope with a force of 415 N. If you pluck the rope at your end, how long will it take the pulse to travel across the ravine to the tree?

Answer: 2.74 s

Var: 1

88) A 2.31-kg rope is stretched between supports that are 10.4 m apart, and has a tension in it of 49.2 N. If one end of the rope is slightly tweaked, how long will it take for the resulting disturbance to reach the other end?

A) 0.699 s

B) 0.720 s

C) 0.664 s

D) 0.615 s

Answer: A

Var: 50+

89) A 1.1-kg uniform bar of metal is 0.40 m long and has a diameter of 2.0 cm. When someone bangs one end of this bar, a 1.5 MHz shock wave is travels along the length of the bar and reaches the other end in 0.12 ms. What is the wavelength of the shock wave in the metal?

A) 2.2 mm

B) 2.6 mm

C) 3.0 mm

D) 3.4 mm

E) 3.8 mm

Answer: A

Var: 1

90) A 10-gram wire that is 6.0 m long is under tension. When a transverse wave of frequency 280 Hz travels along the wire, its wavelength is 0.60 m, and its amplitude is 8.4 mm. How much time does it take for a crest of the transverse wave to travel the length of the wire?

A) 36 ms

B) 31 ms

C) 40 ms

D) 44 ms

E) 49 ms

Answer: A

Var: 50+

91) A 90-gram wire that is 1.0 m long is under tension. When a transverse wave of frequency 890 Hz travels down the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the tension in the wire?

A) 710 N

B) 820 N

C) 930 N

D) 1000 N

E) 1100 N

Answer: A

Var: 50+

92) An earthquake generates three kinds of waves: surface waves (L-waves), which are the slowest and weakest, shear (S) waves, which are transverse waves and carry most of the energy, and pressure (P) waves, which are longitudinal waves and are the fastest. The speed of P waves is approximately 7 km/s, and that of S waves is about 4 km/s. People do not generally feel the P waves, but animals seem to be sensitive to them. If a person reports that her dog started barking 20 seconds "before the earthquake," then approximately how far was the origin of the earthquake?

A) 100 km

B) 200 km

C) 300 km

D) 400 km

E) 500 km

Answer: B

Var: 1

93) A 15-m rope is pulled taut with a tension of 140 N. It takes 0.545 s for a wave to propagate along the rope. What is the mass of the rope?

A) 1.7 kg

B) 2.1 kg

C) 2.8 kg

D) 5.1 kg

E) 3.2 kg

Answer: C

Var: 1

94) Two steel wires are stretched with the same tension. The first wire has a diameter of 0.610 mm and the second wire has a diameter of 0.910 mm. If the speed of waves traveling along the first wire is 54.0 m/s, what is the speed of waves traveling along the second wire?

A) 24.9 m/s

B) 27.2 m/s

C) 36.2 m/s

D) 81.0 m/s

E) 100 m/s

Answer: C

Var: 5

95) A crane lifts a 2500-kg beam at a steady rate of 15 cm/s using a steel cable whose mass per unit length is 0.65 kg/m. What is the speed of transverse waves on this cable?

A) 230 m/s

B) 580 m/s

C) 1200 m/s

D) 1900 m/s

E) 190 m/s

Answer: E

Var: 1

96) A crane lifts a 2500-kg beam using a steel cable whose mass per unit length is 0.650 kg/m. What is the speed of transverse waves on this cable if the upward acceleration of the beam is a steady 3.00 m/s2?

A) 194 m/s

B) 578 m/s

C) 1220 m/s

D) 1880 m/s

E) 222 m/s

Answer: E

Var: 1

97) A wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N. When a transverse wave travels on the wire, its wavelength is 0.10 m and its amplitude is 6.5 mm. What is the frequency of this wave?

A) 890 Hz

B) 920 Hz

C) 1000 Hz

D) 1200 Hz

E) 1500 Hz

Answer: A

Var: 1

98) What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is 8.60 × 103 kg/m3.

A) 0.121 m/s

B) 100 m/s

C) 136 m/s

D) 500 m/s

E) 68.8 m/s

Answer: C

Var: 1

99) The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What are the (a) wavelength and (b) period of this wave?

Answer: (a) 1.93 m (b) 0.870 s

Var: 1

100) The vertical displacement y(x,t) of a horizontal string aligned along the x-axis is given by the equation y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 s-1)t]. What are the (a) speed and (b) amplitude of this wave?

Answer: (a) 2.22 m/s (b) 6.00 mm

Var: 1

101) Find the speed of an ocean wave whose displacement is given by the equation [pic] where x and y are in meters and t is in seconds.

A) 2.5 m/s

B) 1.9 m/s

C) 3.5 m/s

D) 4.5 m/s

Answer: A

Var: 50+

102) What are the wavelength (in meters) and frequency (in hertz) of a wave whose displacement is given by the equation y = 0.5 sin(0.20x + 120t), where x and y are in meters and t is in seconds?

A) 10 m, 0.50 Hz

B) 5.0 m, 10 Hz

C) 19 m, 120 Hz

D) 31 m, 19 Hz

E) 0.20 m, 120[pic] Hz

Answer: D

Var: 1

103) Light from a laser forms a 1.31-mm diameter spot on a wall. If the light intensity in the spot is [pic] what is the power output of the laser? Assume that all the light emitted by the laser hits the spot.

A) 21.3 mW

B) 13.2 mW

C) 17.9 mW

D) 24.7 mW

Answer: A

Var: 50+

104) Calculate the light intensity 1.45 m from a light bulb that radiates 100 W equally in all directions.

A) 3.78 W/m2

B) 4.36 W/m2

C) 47.6 W/m2

D) 54.7 W/m2

Answer: A

Var: 1

105) The average intensity of sunlight impinging on Earth is measured to be about 1.4 kW/m2. What is the power of sunlight emitted by the sun? (Earth-Sun distance = 1.5 × 108 km, Earth radius = 6.4 × 103 km)

A) 4.0 × 1026 W

B) 3.2 × 1022 W

C) 7.2 × 1014 W

D) 7.6 × 108 W

Answer: A

Var: 1

106) A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m.

(a) What is the speed of waves on the string when it is plucked?

(b) What is the string's fundamental frequency of vibration when plucked?

(c) At what other frequencies will this string vibrate?

Answer: (a) 143 m/s (b) 110 Hz (c) f = m(110 Hz), m = 2, 3, 4,

Var: 1

107) Standing waves of frequency 17 Hz are produced on a string that has a mass per unit length of [pic] To what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.87 m apart?

Answer: 14 N

Var: 50+

108) The speed of propagation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s. Which one of the following is not a resonant frequency of this string?

A) 25 Hz

B) 50 Hz

C) 100 Hz

D) 200 Hz

Answer: A

Var: 1

109) A string of linear density 1.5 g/m is under a tension of 20 N. What should be its length if its fundamental resonance frequency is 220 Hz?

A) 0.26 m

B) 0.96 m

C) 1.1 m

D) 1.2 m

Answer: A

Var: 1

110) Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when the tension in it is 50.0 N.

A) 132 Hz, 264 Hz, 395 Hz

B) 66 Hz, 132 Hz, 198 Hz

C) 264 Hz, 528 Hz, 792 Hz

D) none of the above

Answer: A

Var: 1

111) 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 speed of traveling waves on this string.

(d) Determine the fundamental frequency of this string.

Answer: (a) 0.50 m (b) 1.0 m (c) 85 m/s (d) 17 Hz

Var: 1

112) What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g.

A) 517 Hz

B) 234 Hz

C) 181 Hz

D) 312 Hz

E) 366 Hz

Answer: C

Var: 1

113) A 25-g string is stretched with a tension of 43 N between two fixed points 12 m apart. What is the frequency of the second harmonic?

A) 6.0 Hz

B) 12 Hz

C) 18 Hz

D) 24 Hz

E) 36 Hz

Answer: B

Var: 1

114) A 0.588-m string is tightly clamped at both ends. If the lowest standing wave frequency of the string is [pic] how fast do waves travel on this string?

A) 383 m/s

B) 475 m/s

C) 582 m/s

D) 724 m/s

Answer: A

Var: 50+

115) A string that is 2.0 meters long is fixed at both ends and tightened until the wave speed is [pic] What is the frequency of the standing wave shown in the figure?

[pic]

A) 27 Hz

B) 54 Hz

C) 81 Hz

D) 110 Hz

Answer: A

Var: 50+

116) A standing wave is oscillating at 950 Hz on a string, as shown in the figure. What is the wave speed?

[pic]

A) 380 m/s

B) 570 m/s

C) 290 m/s

D) 190 m/s

Answer: A

Var: 50+

117) A guitar-like stringed instrument has a string that is 16 cm long. It sounds the musical note A (440 Hz) when played without fingering. By what distance should you shorten it to play the note C (523 Hz)?

A) 2.5 cm

B) 1.7 cm

C) 3.4 cm

D) 4.2 cm

Answer: A

Var: 50+

118) A 4.0-g string is 0.36 m long and is under tension. The string vibrates at 500 Hz in its third harmonic. What is the wavelength of the standing wave in the string?

A) 0.24 m

B) 0.36 m

C) 0.54 m

D) 0.72 m

E) 0.90 m

Answer: A

Var: 50+

119) A 4.0-g string is 0.39 m long and is under tension. The string vibrates at 600 Hz in its third harmonic. What is the tension in this string?

A) 250 N

B) 200 N

C) 160 N

D) 290 N

E) 340 N

Answer: A

Var: 50+

120) One of the harmonics of a string fixed at both ends has a frequency of 52.2 Hz and the next higher harmonic has a frequency of 60.9 Hz. What is the fundamental frequency of the string?

A) 26.1 Hz

B) 8.7 Hz

C) 4.35 Hz

D) 30.4 Hz

E) 17.4 Hz

Answer: B

Var: 1

121) If the frequency of a violin string is to be increased by 20%, what change in tension must be applied?

A) 44%

B) 20%

C) 4.5%

D) 10%

Answer: A

Var: 1

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