Questions for Review
1. The decibel scale is useful because of the wide dynamic range of human hearing. The intensity of a very soft sound, to the average person, is many times less than the intensity of a very loud sound, typically a trillion times less, or 10¹² times less. Thus, it's useful to use decibels because 10 dB corresponds to a factor of 10 in intensity, while 20 dB corresponds to a factor of 100 in intensity. In this way large ratios are effectively compressed into a linear scale.

2. Frequency response refers to the sensitivity of a device to a particular frequency. Using the tape deck as an example, if you input signals at a steady amplitude for a wide range of frequencies, a "flat" response would mean that the tape deck would record each frequency at the same level. If some recorded signals are above or below the average level, this would indicate a frequency response that weights certain frequencies more than others.

3. The loudness switch on a preamplifier passes the signal through a circuit that boosts both very low and very high frequencies, to account for the fact that at low listening levels the ear's sensitivity to different frequencies is highly variable, and is particularly weak for low and for very high frequencies.

4. The frequency response of the human ear is not very flat at all. We aren't sensitive to low frequencies, a feature that may have evolved to help block common sounds that may be disruptive, such as digestion. The material of the eardrum is not made for vibrating at very high frequencies. In between, there are resonances in the ear canal at around 3 kHz and 9 kHz that enhance our sensitivity to sounds at those frequencies.

5. An increase of 100 dB in intensity corresponds to 100/10 = 10 orders of magnitude, or 10¹⁰. If the threshold of hearing at 1 kHz is defined to be 10^-12 W/m², the sound that is 10¹⁰ times higher in intensity would be 10^-2 W/m².

6. The dynamic range of a CD player is typically around 90 dB, while that of a phono is around 50 dB. The difference 90-50 = 40 dB corresponds to a power difference of 10⁴. If the average person hears a doubling of loudness for a 10 dB intensity increase, 40 dB corresponds to four doublings, or a loudness increase of 2⁴ = 2x2x2x2 = 16 times louder.

7. Sound waves can be produced over a very wide range, from below the threshold for human hearing to well above it.

8. Humans are very sensitive to sounds at around 3 kHz because the outer ear is like a tube that is closed at one end, at if we assume its length to be, on average, about 3 cm, the lowest resonant frequency of such a tube would be 344 m/s divided by 4 x 0.03 m, or 344/0.12 Hz, ~ 3 kHz.

9. To produce a sound two times louder the power level must be increased by around 10 dB. This corresponds to 1 factor of ten increase in power, or 10¹ = 10 times more power.

10. A decrease of intensity level by 20 dB corresponds to a decrease of 10^-2 = 1/100 = 0.01. Since intensity is proportional to sound pressure amplitude squared, the pressure decrease would be 10^-1, or 0.1 times smaller.

Exercises
1. D. ~130 dB
2. B. The sound is 16 times louder
3. C. 60 dB
4. D. 5 Watts
5. B. 32 times louder
6. D. 4 times less
7. D. increases the loudness of only the low and high frequencies at low volume levels
8. A. only slightly louder
9. A. two times louder than on X
10. ranked best to worst: B. X, Y, Z, X
11. C. about 10 dB (it's not easy to read the graph, but it's possible)
12. C. LOUDNESS switch controls certain frequencies by certain amounts while VOLUME switch controls all the frequencies by any amount
13. A. 0 dB
14. B. 1 dB
15. A. 70 dB
16. C. 1.5 Watts/1000 = 0.0015 Watt
17. B. 50 dB
18. A. the frequency response of the human ear is almost flat then
19. B. ear drums cannot move that many times per second
20. C. 10,000