Question 1

Waves on a string: The density of aluminum is 2700 kg/m3. If transverse waves propagate at   in a   aluminum wire, what is the tension on the wire?

Accepted Answer

A)  52 N 
B)  31 N 
C)  42 N 
D)  62 N 
A)  52 N 
B)  31 N 
C)  42 N 
D)  62 N A

Question 2

Shock waves: A jet aircraft, in level flight at constant speed, is observed directly overhead. A sonic boom is heard   later, at which time the line of sight to the aircraft forms a 51° angle with respect to the horizontal. The speed of sound is 325 m/s. The altitude of the aircraft is closest to

Accepted Answer

A)  6700 m. 
B)  5400 m. 
C)  8300 m. 
D)  2700 m. 
E)  13,000 m. 
A)  6700 m. 
B)  5400 m. 
C)  8300 m. 
D)  2700 m. 
E)  13,000 m. A

Question 3

Standing waves on a string: Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 Hz. The other is producing a frequency of 448.4 Hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz?

Accepted Answer

A)  +1.9% 
B)  -1.9% 
C)  +3.7% 
D)  -3.7% 
E)  +8.4% 
A)  +1.9% 
B)  -1.9% 
C)  +3.7% 
D)  -3.7% 
E)  +8.4% D

Question 4

Standing sound waves: One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column?

Accepted Answer

A)  32 Hz 
B)  64 Hz 
C)  88 Hz 
D)  128 Hz 
E)  256 Hz 
A)  32 Hz 
B)  64 Hz 
C)  88 Hz 
D)  128 Hz 
E)  256 Hz

Question 5

Sound level: The intensity level of a "Super-Silent" power lawn mower at a distance of 1.0 m is 100 dB. You wake up one morning to find that four of your neighbors are all mowing their lawns using identical "Super-Silent" mowers. When they are each 20 m from your open bedroom window, what is the intensity level of the sound in your bedroom? You can neglect any absorption, reflection, or interference of the sound. The lowest detectable intensity is 1.0 × 10-12 W/m2.

Accepted Answer

A)  80 dB 
B)  104 dB 
C)  400 dB 
D)  50 dB 
E)  40 dB 
A)  80 dB 
B)  104 dB 
C)  400 dB 
D)  50 dB 
E)  40 dB

Question 6

Standing sound waves: The speed of sound in the air inside a 0.640-m long gas column is 340 m/s. What is the fundamental resonant frequency of this air column if it is
(a) open at one end and closed at the other end?
(b) open at both ends?

Accepted Answer

(a) 133 Hz

Question 7

Intensity: Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light, assuming that the light radiates uniformly in all directions.

Accepted Answer

A)  3.49 W/m2 
B)  4.01 W/m2 
C)  43.9 W/m2 
D)  50.5 W/m2 
A)  3.49 W/m2 
B)  4.01 W/m2 
C)  43.9 W/m2 
D)  50.5 W/m2

Question 8

Waves on a string: A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope?

Accepted Answer

A)  1.00 kg 
B)  1.25 kg 
C)  2.25 kg 
D)  2.50 kg 
E)  1.12 kg 
A)  1.00 kg 
B)  1.25 kg 
C)  2.25 kg 
D)  2.50 kg 
E)  1.12 kg

Question 9

Shock waves: An airplane flying faster than the speed of sound of 340 m/s produces a shock wave that makes an angle of 50° with the direction the plane is flying. What is the speed of the plane?

Accepted Answer

A)  490 m/s 
B)  530 m/s 
C)  390 m/s 
D)  440 m/s 
E)  405 m/s 
A)  490 m/s 
B)  530 m/s 
C)  390 m/s 
D)  440 m/s 
E)  405 m/s

Question 10

Mathematics of traveling waves: The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 rad/s)t].
(a) What is the minimum time for each complete cycle of the wave?
(b) What is the distance between adjacent crests of the wave?
(c) How fast does this wave travel

Accepted Answer

(a) 0.870

Question 11

Mathematics of traveling waves: Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x - 21t)
II: y = 0.15 sin(6x + 42t)
III: y = 0.13 cos(6x + 21t)
IV: y = -0.27 sin(3x - 42t)
Which of these waves have the same period?

Accepted Answer

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. 
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.

Question 12

Standing waves on a string: A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?

Accepted Answer

A)  Both pulses are right side up. 
B)  The reflected pulse returns right side up while the transmitted pulse is inverted. 
C)  The reflected pulse returns inverted while the transmitted pulse is right side up. 
D)  Both pulses are inverted. 
A)  Both pulses are right side up. 
B)  The reflected pulse returns right side up while the transmitted pulse is inverted. 
C)  The reflected pulse returns inverted while the transmitted pulse is right side up. 
D)  Both pulses are inverted.

Question 13

Mathematics of traveling waves: The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

Accepted Answer

A)  4.0 Hz 
B)  0.50 Hz 
C)  3.0 Hz 
D)  0.33 Hz 
E)  0.25 Hz 
A)  4.0 Hz 
B)  0.50 Hz 
C)  3.0 Hz 
D)  0.33 Hz 
E)  0.25 Hz

Question 14

Waves on a string: A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to

Accepted Answer

A)  47,000 m/s2. 
B)  41,000 m/s2. 
C)  35,000 m/s2. 
D)  29,000 m/s2. 
E)  53,000 m/s2. 
A)  47,000 m/s2. 
B)  41,000 m/s2. 
C)  35,000 m/s2. 
D)  29,000 m/s2. 
E)  53,000 m/s2.

Question 15

Mathematics of traveling waves: A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)], where all quantities are in SI units. The maximum speed of a particle of the string is closest to

Accepted Answer

A)  0.33 m/s. 
B)  0.43 m/s. 
C)  0.53 m/s. 
D)  0.64 m/s. 
E)  0.74 m/s. 
A)  0.33 m/s. 
B)  0.43 m/s. 
C)  0.53 m/s. 
D)  0.64 m/s. 
E)  0.74 m/s.

Question 16

Mathematics of traveling waves: Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t) = 3.7 cos(2.2x - 5.6t), where all quantities are in SI units.

Accepted Answer

A)  2.5 m/s 
B)  1.9 m/s 
C)  3.5 m/s 
D)  4.5 m/s 
A)  2.5 m/s 
B)  1.9 m/s 
C)  3.5 m/s 
D)  4.5 m/s

Question 17

Interference: Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s.

Accepted Answer

A)  211 Hz 
B)  256 Hz 
C)  422 Hz 
D)  512 Hz 
E)  674 Hz 
A)  211 Hz 
B)  256 Hz 
C)  422 Hz 
D)  512 Hz 
E)  674 Hz

Question 18

Standing waves on a string: Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same

Accepted Answer

A)  wavelength. 
B)  velocity. 
C)  frequency. 
D)  amplitude. 
E)  More than one of the above is true. 
A)  wavelength. 
B)  velocity. 
C)  frequency. 
D)  amplitude. 
E)  More than one of the above is true.

Question 19

Standing waves on a string: A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

Accepted Answer

A)  Both pulses are right side up. 
B)  The reflected pulse returns right side up while the transmitted pulse is inverted. 
C)  The reflected pulse returns inverted while the transmitted pulse is right side up. 
D)  Both pulses are inverted. 
A)  Both pulses are right side up. 
B)  The reflected pulse returns right side up while the transmitted pulse is inverted. 
C)  The reflected pulse returns inverted while the transmitted pulse is right side up. 
D)  Both pulses are inverted.

Question 20

Mathematics of traveling waves: For the wave shown in the figure, the frequency is

Accepted Answer

A)  0.5 Hz. 
B)  1 Hz. 
C)  2 Hz. 
D)  4 Hz. 
E)  unable to be determined from the given information. 
A)  0.5 Hz. 
B)  1 Hz. 
C)  2 Hz. 
D)  4 Hz. 
E)  unable to be determined from the given information.

Exam 14: Periodic Motion

Waves on a string: The density of aluminum is 2700 kg/m3. If transverse waves propagate at in a aluminum wire, what is the tension on the wire?

Shock waves: A jet aircraft, in level flight at constant speed, is observed directly overhead. A sonic boom is heard later, at which time the line of sight to the aircraft forms a 51° angle with respect to the horizontal. The speed of sound is 325 m/s. The altitude of the aircraft is closest to

Standing sound waves: One of the harmonics of a column of air open at one end and closed at the other has a frequency of 448 Hz and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column?

Standing sound waves: The speed of sound in the air inside a 0.640-m long gas column is 340 m/s. What is the fundamental resonant frequency of this air column if it is (a) open at one end and closed at the other end? (b) open at both ends?

Intensity: Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light, assuming that the light radiates uniformly in all directions.

Waves on a string: A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope?

Shock waves: An airplane flying faster than the speed of sound of 340 m/s produces a shock wave that makes an angle of 50° with the direction the plane is flying. What is the speed of the plane?

Standing waves on a string: A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?

Mathematics of traveling waves: The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

Waves on a string: A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to

Mathematics of traveling waves: Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t) = 3.7 cos(2.2x - 5.6t), where all quantities are in SI units.

Standing waves on a string: Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same

Standing waves on a string: A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

Mathematics of traveling waves: For the wave shown in the figure, the frequency is

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Waves on a string: The density of aluminum is 2700 kg/m³. If transverse waves propagate at in a aluminum wire, what is the tension on the wire?