# Synthesis Theory I: Assignment 2

Do all of the following problems.
1. Plot the the function y(t) = A cos(2 pi f t + phi) using the values A = 0.5, f = 400 Hz, and phi = 0.
2. What are the physical meanings of the symbols "A", "f", and "phi" in problem 1?
3. How do the physical properties of a sinusoid listed in problem 2 relate to human hearing?
4. What is the minimum sampling frequency (theoretically) necessary to correctly sample the sinusoid in problem 1? In practice a filter guard band of at least 5% of the sampling frequency is necessary to prevent aliasing. What is the minimum sampling frequency (practically) necessary to sample the 400 Hz sinusoid?
5. Sample the sinusoid in problem 1 with a sampling frequency of 1000 Hz. What is the sampling period in seconds? What is the period of the 400 Hz sinusoid in seconds? Give a table of the first 5 samples.
 time 1: sample 1: time 2: sample 2: time 3: sample 3: time 4: sample 4: time 5: sample 5:
6. What is the mathematical definition of decibels for amplitude? for energy?
7. If a sound has twice the amplitude of the reference amplitude, what it the dB value for the sound?
8. Consider the height of a person to be the reference height (amplitude) of 2 meters. What are the sizes of the following items on the dB scale.
1. humans (2 meters)
2. giraffe (7 meters)
3. blue whale (30 meters)
4. giant sequoia trees (100 meters)
5. distance from Baltimore to Washington (56,000 meters)
6. distance from Baltimore to New York (274,000 meters)
7. distance from Baltimore to San Francisco (3,965,000 meters)
8. diameter of the Earth (12,756,000 meters)
9. diameter of the Sun (1,400,000,000 meters)
10. distance from the Sun to the Earth (150,000,000,000 meters)
11. distance from the Sun to Pluto (5,890,000,000,000 meters)
12. diameter of the Milky Way galaxy (946,000,000,000,000,000,000 meters)
13. diameter of the universe (230,000,000,000,000,000,000,000,000 meters)
14. cat (0.3 meters)
15. mouse (0.03 meters)
16. bacteria (0.000,001 meters)
17. virus (0.000,000,1 meters)
18. atom of hydrogen (0.000,000,000,1 meters)
19. neutron (0.000,000,000,000,006 meters)
9. What are the decimal values of the following hexadecimal numbers:
```      0xff =
0x0a =
0x10 =
0x7f =
```
10. Convert the following binary or hexadecimal numbers into hex or binary form:
```     binary 1111 =       hex
hex      80 =       binary
binary 0000 =       hex
hex      ff =       binary
hex      a7 =       binary
binary 1001,1000,0000,1111 =        hex
```
11. If the range of hearing is characterized as being from 0 dB(SPL) to 120 dB(SPL), the dynamic range of hearing is 120 dB. (1) How many dB of dynamic range is gained by each bit of data added to the resolution of a soundfile? How many bits would each soundfile sample need in order to match the dynamic range of hearing?
12. What is big-endian and little-endian? What is the decimal value of the following two hexadecimal bytes if they are in (1) little endian form (2) big endian form:
```          3C,7E
```
13. Record at least 10 words using your own voice and save them into a computer soundfile. Make either one soundfile, or 10 separate files for each word. These will be used for demos in the wavetable part of class. Place the sounds on mambo.peabody.jhu.edu, e-mail them to me, or give me a copy of the soundfiles on CDROM.

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