Homework 2 -- due Sept. 24

Answer on a separate sheet of paper (printout of this page does not have enough room for the answers). Be sure to put your name (not your code) on your answer sheet.

1. In problem 1, homework 1 you found that the frequency of a bus on the lot HH - Metro route is approximatly 7 × 10-4 Hz. Assume that the (average) speed of these "bus waves" is 7 m/s (about 11 mph).
  1. What is the wavelength of these waves?
  2. What therefore should be the distance lot HH -- Metro station?

2. Text, Chapter 2, problem 4

3. Text, Chapter 2, problem 5

4. You live by a highway, but fortunately the highway department has built one of those sound barrier walls that we see increasingly often around highways. This cuts down the noise of the cars considerably, but does not eliminate it completely. However, you cannot see the cars at all.

  1. If waves travel in straight lines, you would expect no sound wave from cars to get to you (since you can't see the car along a straight-line light path). Why do you hear them anyway?
  2. Which type of sound do you expect to get to you more easily, the scream of a small child in the back seat of a passing car, or the sub-bass of a powerful car stereo? Why?

5.

  1. Do problem 9c from Chapter 1, drawing carefully. The two waves should have the same amplitude, for example 1 cm (or 1 inch).
  2. On the same axes, add the two waves point by point, as in Fig, 2-35. Label this wave "sum".
  3. What is the frequency of the sum wave (in terms of the frequency of the components)?
  4. What is the amplitude of the sum (in terms of that of the components, i.e. in cm resp. inches), as read off your sum graph?

6. A short burst of sound (e.g. canon shot) is reflected by a set of steps (as in a football stadium), the reflectors being the steps' risers. There are multiple reflections; each successive reflection is delayed over the previous one by the time it takes sound to travel the extra distance from one riser to the next and back. Take the distance from one riser to the next (width of a tread) to be 35 cm, and the speed of sound as 350 m/s. As a consequence of the multiple reflections, the echo has a definite pitch, of period equal to the time between one reflection and the next.
  1. compute this period
  2. find the frequency of the echo.