Physics 102 -- Final Exam

Physics 102 - Final Exam May 23, 00

Instructions:

This exam consists of 9 printed pages and one NCS Answer Sheet. Before you start, fill in your name in letters and in blacked-out circles on the answer sheet. Then answer Part I (Multiple Choice, questions 1-80) on the answer sheet by filling in one of the corresponding circles. Answer Part II (Quantitative, questions 81-100) on the last sheet of the set you are now reading. Each question is worth one point, for a total of 100 points. Further instructions concerning the quantitative part and posting of grades are on page 8.

Read questions carefully. Only correct answers count toward your grade, there is no penalty for incorrect answers, so it pays to answer all the questions. In the quantitative part it pays to explain your reasoning, for partial credit even if your final answer is wrong.

The exam will last 120 minutes, including the reading of these instructions and handing in of papers. You will hand in only the answer sheet and page 9.

I. Multiple-Choice Questions

1. In order to double the wavelength of a sound wave, you should only

(a) double its amplitude (b) double its frequency

2. When two sine waves that are 180^o out of phase are added together, the amplitude of the sum is

(a) always zero

(b) always less than the amplitude of either wave

(d) always less than the amplitude of the larger wave

(e) always greater than the amplitude of the smaller wave.

3. A sound wave has SIL = 50 dB. Recall that SIL = 10 log([ I/(10^-12W/m²)]). The intensity I of this wave, in W/m², is therefore

(a) 50 (b) 5 (c) 10^-5 (d) 10^-7 (e) 10^-10.

4. A sound wave with SIL = 50 dB is reflected by a cloth-covered wall that absorbs 75% of its intensity. The SIL of the reflected wave is

(a) 75 dB (b) 47 dB (c) 44 dB (d) 25 dB (e) 12.5 dB.

5. Light and sound are both waves; yet we can hear a car that is coming from behind the corner of a building before we can see the car. This is because

(a) sound travels faster than light

(b) since l_sound > l_light, sound diffracts more than light

(d) sound and light interfere, with sound winning out.

6. A moving locomotive is sounding its horn as it crosses a highway. There are people in all directions from the locomotive - in front, in back, to the right and left. Compared to the ``true'' pitch, as heard by the engineer, the horn's pitch heard by these people is

(a) higher (b) lower (c) the same for all of the people

(d) higher for some, true for others, and lower for yet others of the people

The diagram below is a plot of the motion of a mass that is bobbing up and down on a spring. The vertical scale shows the mass's height above the floor, and the horizontal scale shows time. Only part of the motion, starting at 5 sec, is shown. Use this plot to answer questions 7-10.

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Picture Omitted

7. This motion is

(a) not periodic (b) periodic but not simple harmonic

8. How many periods are shown?

(a) one (b) two (c) three (d) four

9. What is the period?

(a) 1 sec (b) 2 sec (c) 4 sec (d) 7 sec (e) 9 sec

10. What is the amplitude?

(a) 1 cm (b) 1.5 cm (c) 2 cm (d) 2.5 cm (e) 4 cm

The plots below show displacement (vertical) vs time (horizontal). Use them to identify the vibrations of questions 11-14.

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11. A square wave, amplitude modulated by a sawtooth wave.

12. A damped harmonic vibration.

13. A triangle wave sampled (and held) at 20 times the frequency of the wave.

14. The type of vibration that is heard as ``beats."

15. The frequency of the note B₄ is close to 500Hz. The period of this vibration is

(a) 500 sec (b) 1 sec (c) 0.2 sec (d) 2 msec (e) none of these

16. A sine wave and a square wave cannot have the same

(a) loudness (b) wavelength (c) frequency (d) tone quality (e) pitch

17. An electric bell is operating in a vacuum. We cannot hear the sound of the bell because

(a) air is needed to conduct the electric current to the bell

(b) the bell's metal cannot vibrate in vacuum

(d) the vacuum jar absorbs the sound

(e) the noise of the pump is louder than the noise of the bell.

18. The wavelength of ``shortwave" radio waves is smaller than that of standard broadcast (AM) radio waves. They both propagate at the same speed. This allows you to conclude that, compared to AM waves, the ``shortwaves" have

(a) lower frequency (b) longer period (c) higher frequency (d) smaller amplitudes

19. When a sound wave enters from air into a metal, in which the speed of sound is much larger than in air, it does not change its

(a) wavelength (b) frequency (c) speed (d) all of these (a-c) change

20. Sound moves at 345 m/sec toward a rock wall, reflects, and returns (as an echo). The roundtrip takes 2 sec. How far away is the wall?

(a) 70 m (b) 170 m (c) 340 m (d) 345 m (e) 350 m

21. Two identical sound sources differ in distance from the listener by ¹/₂l. The result will be

(a) no sound at the listener (b) constructive interference

Questions 22-27 refer to the following figure, showing a stretched string, [ 1/2] m long, fixed at the ends.

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22. The dotted curve shows the vibration of this string in its fundamental mode. The wavelength of this wave is

(a) 0.25 m (b) 0.5 m (c) 1 m (d) 2 m (e) 4 m

23. The vibration is

(a) transverse (b) transposed (c) travelling (d) longitudinal (e) triangular

24. The heavy solid curve shows the vibration of this string at which harmonic number N:

(a) 1 (b) 2 (c) 3 (d) 4 (e) 5

25. How many nodes are there in the vibration of the solid curve?

(a) 1 (b) 2 (c) 3 (d) 4 (e) 5

26. The wave speed on this string is v = 100 m/sec. The fundamental frequency is therefore f =

(a) 25 Hz (b) 50 Hz (c) 75 Hz (d) 100 Hz (e) 200 Hz

27. The tension of the string is made 4 times as large as before. As a consequence (mark the best answer)

(a) the frequency becomes twice what it was before

(b) the period decreases by a factor of two

(d) all of the above.

28. A musical tone of frequency 750 Hz, compared to one of frequency 500 Hz, is

(a) A fourth higher

(b) a fifth higher

(d) an octave and a fifth higher

(e) not higher but lower.

29. A closed and an open pipe have the same fundamental frequency. Which one is longer?

(a) the open pipe (b) the closed pipe (c) they are equally long

(d) depends on the speed of sound

30. The two pipes of the previous question are placed in a gas with a speed of sound greater than the speed of sound in air. What happens to their fundamental frequencies:

(a) the longer pipe increases its fundamental more than the shorter one

(b) the shorter pipe increases its fundamental more than the longer one

(d) both frequencies decrease equally.

31. What is the length of an open pipe whose fundamental is 345 Hz, when the speed of sound is 345 m/sec?

(a) 345 m (b) 3.45 m (c) 1 m (d) [ 1/2] m (e) [ 1/3.5] m

32. If the fundamental resonance of a closed tube is 200 Hz, what is the frequency of the next higher resonance?

(a) 300 Hz (b) 400 Hz (c) 500 Hz (d) 600 Hz (e) 800 Hz

33. A graph showing amplitude of response of a system vs driving frequency is called

(a) resonance curve (b) Fourier spectrum (c) velocity pattern

(d) Lissajous figure (e) sonogram

34. The mathematical statement that any periodic wave of frequency f can be synthesized from sine waves of frequencies f, 2f, 3f, ... is called

(a) Bernoulli's principle (b) Fourier's theorem (c) Helmholtz's equation

(d) Huygens' principle (e) Ohm's law

35. Two waves that have the same Fourier spectrum may differ in

(a) wave shape (b) timbre (tone quality) (c) intensity (d) frequency (pitch)

(e) period

Question 36-39 concern the waves so numbered, shown below. For each wave, mark the letter corresponding to its Fourier spectrum, also shown below. For example, if you think wave 36 has the Fourier spectrum (c) (which it does not), mark C for question 36 on the answer sheet.

The time on each graph in the top row runs from 0 to 1 msec, so that wave 36, for example, has frequency 1000 Hz. The frequency scale on the bottom graphs is 1000 Hz per division. Due to the finite range available, graphs (a) and (b) show only part of the spectrum; these two spectra are meant to continue to higher harmonics, with regularly decreasing amplitudes.

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Picture Omitted

40. Changing only the phase of the component waves in the Fourier synthesizer showed that

(a) tone quality is independent of phase

(b) wave shape is independent of phase

(d) wave shape depends on harmonic content.

41. The envelope generator of a synthesizer is typically used to

(a) generate the audio signal.

(b) achieve a vibrato effect.

(d) provide a trigger for the keyboard.

(e) provide an envelope to mail in the payments for the synthesizer.

42. The critical band for a frequency f is

(a) the band of frequencies that the human ear can hear.

(b) the region along the basilar membrane that responds to the frequency f.

(d) a band made of instruments all tuned to the frequency f.

43. The noise of a diesel locomotive at a distance of 100 ft has an SIL of 100 dB. Assume that the inverse square law is valid. What is the SIL from this locomotive at 200 ft?

(a) 200 dB (b) 25 dB (c) 94 dB (d) 10 dB

44. What would be the noise of two such diesel locomotives at 100 ft?

(a) 200 dB (b) 120 dB (c) 103 dB (d) 102 dB (e) 50 dB

45. Inhaling helium or other gas in which the speed of sound is higher than in air changes a person's voice because

(a) the resonance frequencies of the person's vocal tract change.

(b) helium affects the speech center in the brain.

(d) there is no change, the demo was a fake.

46. A pure tone with frequency 1000 Hz is played. A second pure tone, higher in frequency, is played with the first tone. If two distinct tones are perceived, the second tone must be

(a) a frequency JND away from the first tone

(b) outside the first tone's critical band

(d) the subjective fundamental of the first tone.

47. A 60 watt light bulb is designed to take up 60 W of electrical power when connected to 120 Volts. What is the current through the bulb?

(a) 720 A (b) 120 A (c) 60 A (d) 2 A (e) ¹/₂ A

48. A tape recorder puts a signal of 1.5 V amplitude into an impedance of 50,000 W. The transferred power is therefore

(a) much less than 1 W (b) about 1 W (c) much more than 1 W

49. The acoustical purpose of a baffle around a speaker is

(a) to make the speaker look better

(b) to prevent the wave from the back from interfering destructively with that from the front

(d) to prevent excessive vibration of the speaker cone.

50. In order to put the same power into a 16 W speaker as into a 4 W speaker, the voltage across the 16 W speaker's terminals, compared to that across the 4 W speaker's terminal, has to be

(a) equal (b) twice (c) four times (d) half (e) a quarter

51. The number 12 in binary is 1100. The number 13 in binary is

(a) 1101 (b) 11000 (c) 11111 (d) 1200 (e) 1300

52. The largest number you can write with 10 binary bits is 1111111111, which is approximately 1000 in ordinary, decimal notation. Suppose a CD system used just 10 binary bits, so that the largest amplitude it could record would be about a thousand times the smallest amplitude. Assume that the SIL corresponding to the smallest amplitude is 0 dB and use the formula SIL = SIL₀ + 20 log (A/A₀). What would be the dynamic range in this situation?

(a) 6 dB (b) 20 dB (c) 60 dB (d) 1000 dB (e) 2000 dB

53. The reverberation time was defined to be the time required for sound intensity to decrease by a factor of one million (1,000,000). This is equivalent to a decrease in the SIL by

(a) 6 dB (b) 12 dB (c) 60 dB (d) 120 dB

54. If I increase the sound absorption of a room, for example by covering a tile floor with a carpet, the reverberation time

(a) increases (b) remains the same (c) decreases

(d) depends on whether verbs or nouns are used.

55. Which experiment showed interference:

(a) bell in vacuum (b) beaker breaker

56. We showed a 3 dB increase in SIL by

(a) switching an oscillator, connected to a speaker, manually back and forth by 3 dB.

(b) asking the class to shout until an SIL meter showed an SIL of 3dB.

clap.

(d) playing a tape with a sound that varied by 3dB.

57. Which effect cannot be shown with two audio oscillators feeding into one amplifier and speaker:

(a) Faraday's law of induction (b) critical band

58. We used a hairdryer and ping pong ball to illustrate

(a) the vibration of the ball in the standing wave set up by the hairdryer.

(b) the effect of the humidity of air on the speed of sound.

(d) that the air pressure is less on the side of the ball where the air flows faster.

59. We used a Fourier synthesizer to generate a square wave. We could not get a perfect square wave because

(a) phase errors made it lopsided

(b) amplitude errors made the tops and bottoms rounded rather than flat

(d) we DID get a perfect square wave.

60. In one experiment a wire was suspended between the poles of a permanent magnet. When current was made to flow through the wire

(a) the magnet rotated by 90^o (b) the wire moved away from the magnet

(d) the wire was pulled into the region of the strongest magnetic field.

For the following questions mark A for ``true'' and B for ``false''

61. A steady tone played on a violin is an almost perfect sine wave.

62. Different vowel sounds differ mainly in the relative frequency and amplitude of the first two formants.

63. The threshold of hearing is at 0 phons for all frequencies.

64. A standing wave remains constant, without any change in time whatever.

65. The precedence effect enables us to hear the fundamental frequency of a complex wave, even when that frequency is absent in the Fourier spectrum.

66. In the well-tempered scale, only the octaves are perfect intervals.

67. Light is a longitudinal wave, whereas sound is transverse.

68. A triangle wave contains higher-frequency Fourier components than a sine wave of the same periodicity.

69. In a CD player the disk rotates at a constant linear velocity.

70. In a dynamic loudspeaker the sound is produced by vibration of a permanent magnet.

71. In an audio system, AM-FM tuner, tape recorder, and CD player each requires its own, separate amplifier and loudspeaker.

72. The sounds ``ee'' and ``oo'' cannot be spoken (or sung) in such a way that their Fourier spectrums are alike.

73. Therefore the sounds ``ee'' and ``oo'' cannot be spoken (or sung) at the same pitch.

74. To make the acoustics of an auditorium more live, the wall, ceiling, and floor surfaces should be made as sound absorbent as possible.

75. In white noise all frequencies are present, and all have the same intensity.

76. Attack transients help determine the tone quality of a musical note.

77. The sound quality of a violin is due only to the resonances of its strings; the violin body has no resonances of its own.

78. Percussion instruments have only a single resonance.

79. For two electrical devices connected to the same voltage, the one with the smaller resistance draws the smaller current.

80. In order to avoid interference between different AM stations, each station uses a carrier wave that is different from that of any of the other stations.

Further instructions:

Questions 81-90 are to be answered on the last page (page 9). Write your name in the space provided, and either now or when you finish, detach that page so the single page 9 can be handed in (i.e. without the multiple-choice part I).

If you want your grade posted on the phys102 web site, write ``please post'' below your name and also give a ``secret code'' for yourself under which to post your grade (legibly, please!).

At the very end there is an option for you to fill in answers to questions 81-100 on the answer sheet. You cannot ``lose'' anything (except a small amount of time) by doing so, because we will still look at your drawings and, for possible partial credit, at any written answer of 81-100 on which you did not get a perfect score.

II. Quantitative Questions your name

For these problems, use speed of sound = 345 m/sec.

81-90. a. Draw an open tube, and within it the ``transverse representation" of the velocity pattern for a standing sound wave at harmonic number N = 3:

b. The open tube is 4.2 cm (= 0.042 m) long. Find the frequency of the N = 3 harmonic in Hertz, accurate to five figures (that is, forget about the figures after the decimal point). Show your work below.

c. Draw a closed tube, and within it the ``transverse representation" of the velocity pattern for a standing sound wave at harmonic number N = 3:

d. How long should the closed tube be so that its N = 3 harmonic has the same frequency as that of the of the open tube of part (a)?

91-100. At a distance of 6 m from a source the sound intensity is 4.8×10^-8 W/m² = 0.000000048 W/m².

a. What is the intensity (in W/m²) at 12 m from the source?

b. How far from the source must you move for the intensity to fall to 1/16 of the intensity at 6 m?

c. The SIL of this source at 6 m is 47 dB. What is the SIL at 3 m?

Optional - Help us grade: For question 81-90, mark the five digits of your answer to b., in sequence, in spaces 81-85 of the answer sheet; and mark the two non-zero digits of your answer to d., in sequence, in spaces 86-87 of the answer sheet. Mark spaces 88-90 with A.

For questions 91-100, mark the two non-zero digits of your answer to a., in sequence, in spaces 91-92, and also in spaces 93-94, of the answer sheet; and mark the two non-zero digits of your answer to b., in sequence, in spaces 95-96, as well as 97-98, of the answer sheet; and mark the two digits of your answer to c., in sequence, in spaces 99-100 of the answer sheet.

We will of course still look at your written answers! Thanks, and have a good summer.

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On 13 Dec 2002, 17:30.