Questions for Review
1. Digital recording features many advantages over analog, including: higher signal-to-noise ratio, wider dynamic range, better frequency response, and greater durability in recording and replaying.

2. The dynamic range on a CD is determined by the vertical resolution. Typically, this is at least 16 bits. Since 2¹⁶ = 65,536, there are this many "vertical steps" into which an analog signal can be resolved. The smallest signal other than "0" would correspond to "1," while the largest is 65,535, so the dynamic range is (20 dB)log(65,535) 96 dB.

3. The maximum relative range of amplitudes on a CD follows from the calculation above: It is 65,535:1.

4. An ADC is an "analog-to-digital converter," which takes an analog audio signal and converts it to digital, i.e., to a string of ones and zeroes. A DAC does the reverse, in order to recreate the audio signal from the digitally stored information.

5. The Sampling Theorem states that when digital sampling is used to record waveforms, completely accurate acquisition requires that the sampling rate be at least twice the highest frequency that is recorded. Since the audio range typically includes up to 20,000 Hz, the sampling rate for CD recording and playback is 44,100 Hz. If a rate lower than twice the highest frequency is employed, it will result in aliasing, which is the introduction of extraneous frequencies into the recorded track.

6. A laser is need to read a CD because its light is coherent, that is, all the wavefronts are in phase with one another. This is important because the occurrence of digital "ones" on the disk results from interference between the light reflected from "pits" and "land" on the CD surface, and strong interference signals result only if the exciting light is coherent.

7. A pre-recorded Mini-Disc differs from a CD in two major ways. First, the technique used to discern the digital code on the disk involves sensing the magnetization of the recorded track by a magneto-optical technique, whereby the polarization of the reading laser is rotated by the magnetism of the disk. Second, the data is recorded in a compressed format, in which sounds that are probably not discerned in the full-blown CD recording are left out, thereby decreasing the size of the audio data files.

8. A laser emitting blue rather than infrared light would have a shorter wavelength, and could therefore be focused to a smaller spot. The result is that information could be more tightly packed onto the CD, i.e. the pits could be smaller and more closely spaced, such that a higher storage density would be achieved.

9. Polarization is important in playback of a CD because the light is incident perpendicularly onto the disk and the reflected light must be detected in order to discern the pit-to-land transitions. Thus, the reflected beam overlaps the incident light beam. In order to separate the two beams, a polarizing beam splitter is used in conjunction with a ¼-wave plate. See Fig. 10.22. Horizontally polarized light passes through the ¼-wave plate, causing it to become circularly polarized. When this light is reflected and transmitted again through the ¼-wave plate it becomes vertically polarized, and is reflected at a 90 degree angle to the incident beam by a polarizing beamsplitter cube.

10. The amount of information stored on a CD is limited by its surface area and the size of pits that can be read by the laser. A shorter light wavelength corresponds to a smaller focused beam, which could read smaller pits that then could be more tightly packed onto the disk.

Exercises
1. A. 65,535
2. B. 32 kHz
3. B. 1,411,200
4. B. starts near the center and spirals outward toward the edge
5. D. 32 times louder
6. C. 49 times. the ratio of amplitudes is 7, and power is proportional to amplitude squared
7. C. 44,100/882 = 50 times
8. A. 11001001 = 128+64+8+1 = 201
9. D. a CD's signal must go through a digital-to-analog converter before being sent to speakers
10. A. comparable in size to the wavelength of the laser beam
11. D. its amplitude
12. C. decrease, since the blue wavelength is shorter than the infrared
13. B. 3.8 x 10¹⁴ Hz
14. B. 1,000
15. E. all of the above
16. A. decreases
17. B. shorter than in air
18. C. the question is a little vague. the rotation rate of the CD slows from 500 rpm to 200 rpm, such that the linear speed along the track remains constant.
19. E. all of the above
20. B. 1,411,200 bits per sec x 60 sec per min x 74 min = 6.26 x 10⁹ bits