1-1 Expressions and Formulas

The Michelson and Morley experiment

PROBLEM SET

PROBLEM 1. Suppose an observer detects the frequency of a sound source to be 500 Hz while at rest in the rest frame of the source. Now the observer begins moving at a constant speed in the x-direction, and detects the frequency to become higher by 15 Hz. What is the observer's speed and direction, with respect to the source frame? The speed of sound is 373 m/s.

PROBLEM 2. Suppose an observer detects the frequency of a sound source to be 500 Hz while at rest in the rest frame of the source. Now the observer begins moving at a constant speed in the x-direction, and detects the frequency to become lower by 15 Hz. What is the observer's speed and direction, with respect to the source frame?

PROBLEM 3. What is the wavelength of sound that has a frequency of 500 Hz?

PROBLEM 4. Derive the formula for the Doppler effect

f'sound = fsound(1 + vobs/vsound).

PROBLEM 5. Suppose Michelson and Morley had measured a frequency shift of 15% during the rotation of the apparatus. At what speed would they have calculated the earth was traveling through the ether?

PROBLEM 6. What expected percent change in the frequency should have been observed in the Michelson-Morley experiment if the speed of earth relative to the ether frame was Mach 10--ten times the speed of sound?

PROBLEM 7. Consider the following sine waves, where y is in meters and x is in radians:

y1 = 1 sin (2x)

y2 = 2 sin (x)

y3 = 2 sin (x - p/2)

(a) Graph each equation in the interval 0 £ x £ 2p. You may use the same coordinate system for all three graphs if you color code them.

(b) Graph y1 + y2 on the same coordinate system, using another color.