Physics of Music

Physics 341

Assignment 1

1) A drum is played in a vacuum, and in a room. What would you expect to happen to the frequency of the drum in the vacuum? What would you expect to happen to the damping?

2) A car with bad shock absorbers bounces up and down when it hits a bump. What would you expect to happen to the bouncing frequency if you fill the car with your friends? What would the frequency be of the wheels bouncing if you turned the car upside down?

3) If you made a bell out of thicker metal, what would you expect to happen to the tones that the bell makes.

4) A tunig fork has the wrong frequency. Where would you shave away metal to increase the frequency? Where would you shave it away to decrease the frequency?

5) As you empty a wine bottle, the tone you get when you blow across it changes. How does it change and why? (Note assume that the tone you get while blowing is the same as you would get by ``popping" the top of the bottle. While true, the reason will only come up later in the course). If you lengthen the neck of the bottle, leaving the volume of the bottle the same, what happens to the frequency?

6) What happens to the tone of a beer bottle as you narrow the neck. (This is a tricky situation, which many physicists get wrong).

7)A note has a frequency of 660 Hz. What is its period? Another vibration has a period of 8ms (1ms= 1/1000 sec). What is its frequency?

8) In the following figure, what is the period, the frequency and the amplitude of the signal?

[ Brief table of commonly used prefixes:

• n = nano = $10^{-9}$ = 1/1,000,000,000
• $\mu$ = micro = $10^{-6}$ = 1/1,000,000
• m = milli = $10^{-3}$ = 1/1,000
• c = centi = $10^{-2}$ = 1/100
• d = deci = $10^{-1}$ = 1/10
• h = hecta= $10^2$ = 100
• K = kilo = $10^3$ = 1000
• M = Mega = $10^6$ = 1,000,000
• G = giga = $10^9$ = 1,000,000,000 ]

It is interesting that in scientific notation, names are given only up to Y= Yotta= $10^{24}$, whereas I was told that in classical Japanese there are names for numbers at least all the way up to $10^{52}$. (The Japanese use 10000=$10^4$ as the multiple for names, rather than our 1000.) Why in the 16th century anyone would need to give such a number a name I do not know. This aside is of course totally irrelevant to the course.