Physics 104 Solutions
Symko, Physics of Hi-Fi, Chapter 2


Questions for Review
1. Five types of waves encountered in hi-fi sound recording and reproduction:

2. When sound waves resonate in a tube open at both ends, displacement antinodes occur at each open end because molecules can oscillate in and out of the tube, leading to a series of standing waves with wavelength 2L, L, L, ½ L, etc. Since the frequency is the speed of sound, v, divided by the wavelength, the corresponding frequencies are f = v/2L, 2(v/2L), 3(v/2L), etc., that is, integer multiples of the quantity v/2L. We say that the tube resonates with both even and odd harmonics.

If the tube is closed at one end only, the waveforms are no longer symmetric about the midpoint because of the asymmetry at the two ends. Now there's a displacement antinode at the open end and a displacement node at the closed end. The allowed standing wavelengths are now 4L, 4/3 L, 4/5 L, etc., so the allowed frequencies are v/4L, 3(v/4L), 5(v/4L), that is, only odd harmonics of the fundamental frequency v/4L.

3. Hi-fi components in which resonance occurs:

4. Musical instruments sound different when they play the same note because they have different spectra of overtones or harmonics. Also, the time evolution, including the attack and decay, is characteristic of the particular instrument.

5. Hall acoustics dramatically affect the quality of sound. Rooms have resonances, which are particular frequencies at which standing waves build with particular spatial patterns. Surfaces in the room differentially absorb/reflect sound depending on the sound frequency, which affects the reverberation time. Listeners' hearing is affected by the relative amount of direct sound and reverberant sound they hear. Different reverberation times are required to optimize the sound of different sources, e.g. an organ thrives on a long reverberation time, while the clarity of the spoken voice is enhanced by a short reverberation time.

6. Fourier analysis refers to the process of recording sound and analyzing it for its frequency content. This reveals the different frequencies present in the sound, which can be related to how the source produces sound.

7. Standing waves are recurring spatial patterns of vibrations that don't appear to translate. They occur at specific frequencies that depend upon the geometry, size and material structure of different vibrating objects. Standing waves are supported by objects such as strings, tubes, plates, disks, boxes, and optical cavities, as in the laser.

8. To change the fundamental of a tube open at both ends, you could either change the length of the tube or close one end. Slight changes can also be made by changing the tube diameter.

9. Two waves are in-phase when both their crests and troughs overlap. They are out-of-phase when the crest of one overlaps the trough of the other.

10. The square wave consists of odd harmonics only, with a relative amplitude of 1/n, where n is the harmonic number. The sawtooth consists of both even and odd harmonics, also with relative amplitudes 1/n. So a 100 Hz square wave would contain waves at 100 Hz, 300 Hz, 500 Hz, etc., while a sawtooth wave with the same fundamental would have component waves of 100 Hz, 200 Hz, 300 Hz, 400 Hz, and so on.

Exercises
1. D. transverse wave
2. D. distance a wave travels before it starts to repeat itself
3. B. 688 Hz
4. B. wavelength
5. E. how long it takes to produce a pressure fluctuation
6. A. decrease by a factor of 4
7. B. 1,000 Hz
8. A. 125 m/sec
9. A. 20 Hz to 20 kHz
10. D. two times more power is needed
11. B. 15 x 10-5 Watts
12. B. the angle of reflection equals the angle of incidence
13. A. which is 4 times shorter than in water
14. B. 5 times less
15. A. its frequency will increase due to the Doppler effect
16. A. increase
17. B. 20
18. C. decrease
19. E. there is relative motion between the source and the observer
20. B. the individual note of music become blurred
21. A. mainly reverberant with some direct sound
22. D. constructive interference
23. C. two identical waves traveling in opposite directions and passing through each other
24. C. one wavelength
25. D. because the number and relative amplitude of the harmonics may be different
26. A. Fourier analysis
27. A. displacement antinode
28. D. interference
29. B. 86 Hz
30. E. all of the above are correct
31. A. no sound at the listener
32. C. 258 Hz
33. C. 0.125 meter
34. D. 4
35. D. 37 Hz
36. A. destructive interference
37. A. 3000 Hz
38. B. 21.5 Hz
39. D. cause individual notes to become blurred together, causing an unnatural sound
40. B. toward the normal

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