Modern Physics

Fall 2009

Assignment 1:

· Read chapter 1 by Friday, September 11. This is just a summary of what we knew near the end of the 19^th century. I will spend some time reviewing both mechanical waves and optics. You should study the sections on mechanical waves in your General Physics Textbook and section 5.4 (pp.174-181) in Thornton & Rex.

· Turn in the problems below on Friday, September 18.

1. A steel wire has a length of 0.8m, a mass of 4 grams and has a tension of 40N. It is fixed at both ends. (Watch the mixed units!)

a.) What will be the speed of a transverse wave on the string?

b.) What will be the frequencies of the first two resonant frequencies?

2. A sound wave in air has a pressure variation given by

p(x,t) = 2[Pa] cos( 6px/m – 720pt/s)

where x is distance and t is time. Note that I've included the units of pressure in brackets [Pa]. Find (a) the speed of the wave, (b) the amplitude of the pressure, (c) the wavelength, and (d) the frequency.

3. A string with a linear density of 0.04kg/m, has a tension of 100N. A wave of frequency 12p rad/s has an amplitude of 0.01m as it propagates down the string. What is the average rate at which energy is transmitted down the string, (i.e. the average power)?

4. Write down the expression for a traveling wave (on a string) whose frequency is 9p rad/s and moving in the + x direction with a speed of 40m/s. The amplitude is 1cm.

5. A source emits sound at a frequency of 400Hz. It is moving away from a stationary observer at a speed of 5m/s. What is the frequency heard by the observer if the speed of sound is 340m/s?

6. A source emits sound at a frequency of 1000Hz. It is moving toward a cliff at a speed of 10m/s. It, the source, hears the waves reflected from the cliff. What is the frequency it hears if the speed of sound is 340m/s.

7. Find the spatial form of the first two modes of a vibrating string {i.e. y(x)} that stretches from x = –L/2 to x = +L/2. Assume that the speed of the wave is c. Are the shapes and frequencies the same as the case where the string stretches from x = 0 to x = L?