Queens College, CUNY - PHYSICS 152

Chapter 13—Mechanical Waves

MULTIPLE CHOICE

1)You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 4 cm wide but 7 mm high. You must move your hand up and down once,

1. 1. the same distance up as before, but take a shorter time.
   2. the same distance up as before, but take a longer time.
   3. a smaller distance up, but take a shorter time.
   4. a greater distance up, but take a longer time.
   5. a greater distance up, but take the same time.

                                

 

 

2. You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide but still 5 mm high. You must move your hand up and down once,
   1. the same distance up as before, but take a shorter time.
   2. the same distance up as before, but take a longer time.
   3. a smaller distance up, but take a shorter time.
   4. a greater distance up, but take a longer time.
   5. a greater distance up, but take the same time.

                                

 

3. You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide and 7 mm high. You must move your hand up and down once,
   1. the same distance up as before, but take a shorter time.
   2. the same distance up as before, but take a longer time.
   3. a smaller distance up, but take a shorter time.
   4. a greater distance up, but take a longer time.
   5. a greater distance up, but take the same time.

                                

 

4. A wave generated in a medium is a longitudinal wave when
   1. there is a net transport of matter by the wave.
   2. the molecules of the medium are unable to exert forces on each other.
   3. molecular displacements are parallel to the wave velocity.
   4. molecular displacements are perpendicular to the wave velocity.
   5. the density of the medium is less than the density of water.     
5. The wavelength of light visible to the human eye is on the order of 5 ? 10^?7 m. If the speed of light in air is 3 ? 10⁸ m/s, find the frequency of the lightwave.

a.   3 ? 10⁷ Hz

b. 4 ? 10⁹ Hz

c.   5 ? 10¹¹ Hz

d.  6 ? 10¹⁴ Hz

e.   4 ? 10¹⁵ Hz

                                

 

6. The speed of a 10-kHz sound wave in seawater is approximately 1 500 m/s. What is its wavelength in sea water?
   1. 5.0 cm
   2. 10 cm
   3. 15 cm
   4. 20 cm
   5. 29 cm

                                

 

7. Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect?
   1. 1.5 mm
   2. 3.5 mm
   3. 5.5 mm
   4. 7.5 mm
   5. 9.8 mm

                                

 

8. Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?
   1. 8.0 m/s
   2. 16 m/s
   3. 24 m/s
   4. 30 m/s
   5. 4.0 m/s

                                

 

9. If y = 0.02 sin (30x ? 400t) (SI units), the wave number is
   1. 30 rad/m
   2. 30/2? rad/m

c.   400/2? rad/m

4. 400 rad/m
5. 60? rad/m

                                

 

 

10. For the transverse wave described by                                                  , determine the maximum transverse speed of the particles of the medium.

a.   0.192 m/s

b. 0.6? m/s

3. 9.6 m/s
4. 4 m/s
5. 2 m/s

                                

 

11. Which of the following is a solution to the wave equation,               ? a.

 

2. (cos kx) (sin ?t)
3. e^?x sin ?t
4. e^?x sin (kx ? ?t)
5. e^?x cos t

                                

 

12. Find the period of a wave of 100-m wavelength in deep water where           .
    1. 5.0 s
    2. 8.0 s

c.   12.5 s

d. 15 s

e.   0.125 s

                                

 

13. A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to
    1. increase the tension on the hose and shake the end more times per second.
    2. decrease the tension on the hose and shake the end more times per second.
    3. increase the tension on the hose and shake the end fewer times per second.
    4. decrease the tension on the hose and shake the end fewer times per second.
    5. keep the tension and frequency the same but increase the length of the hose.                        

: Exhibit 16-01

Exhibit 16-1

The figure below shows a sine wave at one point of a string as a function of time.

 

 

 

 

Use the exhibit to answer the following question(s).

 

14. Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

1. 1. d.

 

 

 

 

 

 

1. 2. e.

 

 

 

 

 

 

c.

 

 

 

 

 

 

 

                                

 

15. Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half?
    1. d.

 

 

 

 

 

 

1. 2. e.

 

 

 

 

 

 

c.

 

 

 

 

 

                                  : Exhibit 16-02

Exhibit 16-2

The figure below shows a sine wave on a string at one instant of time.

 

 

 

 

Use this exhibit to answer the following question(s).

 

16. Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?
    1. d.

 

 

 

 

 

 

1. 2. e.

 

 

 

 

 

 

c.

 

 

 

 

 

 

                                

 

17. Refer to Exhibit 16-2. Which of the graphs below shows a wave where the wavelength is twice as large?
    1. d.

1. 2. e.

 

 

 

 

 

 

c.

 

 

 

 

 

 

 

                                

 

18. The wave equation is written down in an exam as

 

 

 

 

From dimensional considerations we see that a.

v² should be replaced by .

b.

 

v² should be replaced by     .

c.   v² should be replaced by v. d.

v² should be replaced by   .

e.

v² should be replaced by  .

                                

 

: Exhibit 16-03

Exhibit 16-3

Four wave functions are given below.

 

I.        y(x, t) = 5sin(4x – 20t + 4)

II.       y(x, t) = 5sin(3x – 12t + 5)

III.      y(x, t) = 5cos(4x + 24t + 6)

IV.     y(x, t) = 14cos(2x – 8t + 3)

 

Use this exhibit to answer the following question(s).

 

19. Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wave speeds, from least to greatest.
    1. IV, II, I, III

b. IV = II, I, III
c.   III, I, II, IV
d. IV, I, II, III
e.   III, IV, II, I

 

20. Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the frequencies of the waves, from least to greatest.
    1. IV, II, I, III
    2. IV = II, I, III
    3. III, I, II, IV
    4. IV, I, II, III
    5. III, IV, II, I

                                

 

21. Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wavelengths, from least to greatest.
    1. IV, II, I, III
    2. IV, I, II, III
    3. I, II, III, IV
    4. IV, II, III = I
    5. I = III, II, IV

                                

 

22. Earthquake waves are classified as P waves and S waves. Which of the following statements is true about these waves?
    1. The P wave is transverse as is the S wave.
    2. The P wave is longitudinal as is the S wave.
    3. The P wave is transverse and the S wave is longitudinal.
    4. The P wave is longitudinal and the S wave is transverse.
    5. Both the P and S waves are mixtures of longitudinal and transverse waves.     
23. What is the expression for the transverse velocity of the wave in a string given by               ? a.

b.

c.

d.

e.

                                

 

24. A boat sounds a fog horn on a day when both the sea water and the air temperature are 25.0? C. The speed of sound in sea water is 1 533 m/s. How much earlier (in s) does a dolphin 1 000 m from the source hear the sound than a person in a boat that is also 1 000 m distant? (Ignore the time it takes the sound to reach the water surface.)

a.   0.652

b.   2.12

c.   2.24

d.   2.77

e.   2.90

                                

 

25. The fundamental frequency of a above middle C on the piano is 440 Hz. This is the tenor high A, but a convenient note in the mid-range of women's voices. When we calculate the wavelength, we find that it is
    1. much shorter than the length of either a man's or woman's lips.
    2. shorter than the length of a man's lips, but about the length of a woman's lips.
    3. longer than a woman's lips, but about the length of a man's lips.
    4. much longer than the length of either a man's or a woman's lips.
    5. about the same length as either a man's or woman's lips.     
26. If y = 0.02 sin (30x ? 400t) (SI units), the velocity of the wave is a.     3/40 m/s

b.   40/3 m/s

c.   60?/400 m/s

d.  400/60? m/s

e.   400 m/s

                                

 

27. A piano string of density 0.005 0 kg/m is under a tension of 1 350 N. Find the velocity with which a wave travels on the string.
    1. 260 m/s
    2. 520 m/s

c.   1 040 m/s

d.   2 080 m/s

e.   4 160 m/s

                                

 

28. A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 ? 10⁴ N, what is the speed of transverse waves on the cable?
    1. 60 m/s
    2. 122 m/s
    3. 244 m/s
    4. 310 m/s

e.   1 500 m/s

                                

 

29. Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength (where the string is fastened at both ends), find the frequency of vibration.
    1. 250 Hz
    2. 500 Hz
    3. 1 000 Hz
    4. 2 000 Hz
    5. 2 500 Hz

                                

30. The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?

a.   0.025 kg

b.   0.049 kg

c.   0.051 kg

d.   0.081 kg

e.   0.037 kg

                                

 

31. Suppose that you were selected for a "Survivor"-type TV show. To help keep your group connected, you suggest that long vines can be tied together and used to transmit signals in cases of emergency. To get the signals to travel faster, you should
    1. select lighter vines.
    2. increase the tension on the vines.
    3. hang weights from the vines at evenly spaced intervals.
    4. do all of the above.
    5. do (a) or (b) above, preferably both.

                                

 

32. The figure below represents a string which has a heavy section and a light section. The mass per unit length of the heavy section is 16 times as large as the mass per unit length of the light section. When the string is under tension, the speed of a pulse traveling in the heavy section is       times the speed of that same pulse traveling in the light section.

 

 

 

 

a.
b.
c.
2 4

 

33. A piano wire of length 1.5 m vibrates so that one-half wavelength is contained on the string. If the frequency of vibration is 65 Hz, the amplitude of vibration is 3.0 mm, and the density is 15 g/m, how much energy is transmitted per second down the wire?
    1. 21 W
    2. 11 W
    3. 5.4 W
    4. 2.2 W
    5. 1.1 W

                                

 

34. To transmit four times as much energy per unit time along a string, you can
    1. double the frequency.
    2. double the amplitude.
    3. increase the tension by a factor of 16.

1. 4. do any one of the above.
   5. do only (a) or (b) above.

                                

 

35. Calculate the pressure amplitude (in N/m²) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5.0 ? 10^?8 m. (? = 0.179 kg/m³, v = 972 m/s.)

a.   3.5 ? 10^?2

b.    1.6 ? 10^?2

c.   2.7 ? 10^?2

d.    4.2 ? 10^?2

e.   2.0 ? 10^?2

                                

 

36. Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 ? 10^?3 N/m². (? = 0.179 kg/m³, v = 972 m/s.)

a.   2.9 ? 10^?10

b.    3.7 ? 10^?10

c.   7.8 ? 10^?9

d.    2.4 ? 10^?9

e.   1.9 ? 10^?10

                                

 

37. The variation in the pressure of helium gas, measured from its equilibrium value, is given by ?P = 2.9

? 10^?5 cos (6.20x ? 3 000t) where x and t have units m and s, and ?P is measured in N/m². Determine the frequency (in Hz) of the wave.

a.   1 500

b. 477

c.   1.01

d.   0.32

e.   239

                                

 

38. The variation in the pressure of helium gas, measured from its equilibrium value, is given by ?P = 2.9

? 10^?5 cos (6.20x ? 3 000t) where x and t have units m and s, and ?P is measured in N/m². Determine the wavelength (in m) of the wave.

a.   1 500

b. 0.32

c.   477

d.   1.01

e.   0.50

                                

 

39. The variation in the pressure of helium gas, measured from its equilibrium value, is given by ?P = 2.9

? 10^?5 cos (6.20x ? 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave. a.           1 515

b.   153

c.   484

d.   828

e.   101

                                

 

40. A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.)

a.   220

b.   448

c.   526

d.   552

e.   383

                                

 

41. A car moving at 36 m/s passes a stationary police car whose siren has a frequency of 500 hz. What is the change in the frequency (in Hz) heard by an observer in the moving car as he passes the police car? (The speed of sound in air is 343 m/s.)

a.   416

b.   208

c.   105

d. 52

e.   552

                                

 

42. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck as the police car approaches the truck? (The speed of sound in air is 343 m/s.)

a.   396

b.   636

c.   361

d.   393

e.   617

                                

 

43. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)

a.   361

b.   636

c.   393

d.   396

e.   383

                                

 

44. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the change in frequency (in Hz) heard by an observer in the truck as the two vehicles pass each other? (The speed of sound in air is 343 m/s.)

a.   242

b.   238

c.   240

d.   236

e.   234

                                

 

45. When you hear the horn of a car that is approaching you, the frequency that you hear is larger than that heard by a person in the car because for the sound you hear
    1. wave crests are farther apart by the distance the car travels in one period.
    2. wave crests are closer together by the distance the car travels in one period.
    3. the car gets ahead of each wave crest before it emits the next one.
    4. the speed of sound in air is increased by the speed of the car.
    5. a speeding car emits more wavecrests in each period.     
46. While you are sounding a tone on a toy whistle, you notice a friend running toward you. If you want her to hear the same frequency that you hear even though she is approaching, you must
    1. stay put.
    2. run towards her at the same speed.
    3. run away from her at the same speed.
    4. stay put and play a note of higher frequency.
    5. run towards her and play a note of higher frequency.     
47. A person standing in the street is unaware of a bird dropping that is falling from a point directly above him with increasing velocity. If the dropping were producing sound of a fixed frequency, as it approaches the person would hear the sound
    1. drop in frequency.
    2. stay at the same frequency.
    3. increase in frequency.
    4. decrease in loudness.
    5. stay at the same loudness.

                                

 

48. (Do not try the following: it could kill you. This question is only about a hypothetical possibility.) If you were standing below an object emitting a fixed frequency sound falling at terminal velocity, as it approached you, you would hear the sound
    1. drop in frequency.
    2. stay at the same frequency.
    3. increase in frequency.
    4. decrease in loudness.
    5. stay at the same loudness.

                                

 

49. A friend hands you an equation sheet with the following equation for the Doppler effect:

 

. This version of the equation is correct with signs as given only if

1. 1. the observer and source are approaching each other.
   2. the observer is approaching the source while the source is moving away from the observer.
   3. the observer is moving away from the source while the source is approaching the observer.
   4. the observer and source are moving away from each other.
   5. the observer and source are moving in perpendicular directions.

                                

 

50. An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center?
    1. 88.9 km
    2. 1 200 km
    3. 675 km
    4. 240 km
    5. 480 km

                                

 

PROBLEM

 

51. If the breakers at a beach are separated by 5.0 m and hit shore with a frequency of 0.20 Hz, with what speed are they traveling?

 

 

 

 

52. 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 in air is 340 m/s, what is the smallest size insect they can detect?

 

 

 

 

53. A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes 0.8 s for the wave to travel the 20 m to the opposite tower. If one meter of the rope has a mass of 0.35 kg, find the tension in the tightrope.

 

 

 

 

54. A bat, flying at 5.00 m/s, emits a chirp at 40.0 kHz. If this sound pulse is reflected by a wall, what is the frequency of the echo received by the bat? (v_sound = 340 m/s.)

 

 

 

 

55. An airplane traveling at half the speed of sound emits sound at a frequency of 5 000 Hz. At what frequency does a stationary listener hear the sound as the plane approaches, and after it passes by? Assume the airplane is not flying very high.