Homework 3 -- due Oct. 1

1. In the Quincke's interference tube experiment (text p. 40) one of the tubes is 20 cm longer than the other. When the speaker puts out 1000 Hz, no sound reaches the microphone. What is (probably) the speed of sound in the gas that fills the tubes? (Show your work!)

2. Text, Chapter 3, problem 2c, leaving out the last sentence

3.

  1. Study and understand Figure 3-6. Then reproduce parts (3) and (4) and a corresponding figure for the time halfway between that of (3) and (4), labeled as (3.5) A glance at Figure 3-8 will help.
  2. Repeat, replacing the sine wave by an equal number of cycles of a sawtooth wave.

Hint: You may print out this figure, in which the incident waves (solid line) and the reflected wave (dotted) are already drawn for you, on the same axis (not one underneath the other as in Figure 3-6). You draw the sum wave on the same axis. Most of this is very simple, but pay particular attention to stage (3.5) of the sawtooth wave and draw the sum wave carefully. Note that the sum is not well defined where one of the summands has a vertical part; it is therefore appropriate to figure the sum just before and just behind the vertical part.

4. Text, Chaper 2, problem 6

5. We have a source of sound emitting a constant frequency (according to a co-moving observer). Can it move in such a way that some (most) stationary observers hear a Doppler effect, but other (fewer) stationary observers hear a constant, un-shifted frequency? Along what kind of curve should such a source move?

6. The space shuttle moves straight up with a velocity exceeding the speed of sound. Explain, by means of a diagram, why an observer near the launching pad does not hear a sonic boom.