# Michelson-Morley Experiment question

1. Oct 14, 2011

### superspartan9

1. The problem statement, all variables and given/known data
Consider an apparatus for performing a Michelson-Morley experiment to measure the speed of sound in the laboratory. A sound wave of frequency 3,600 Hz replaces light. The speed of sound in air is 330 m/s. The arms of the interferometer are 2m long, and the apparatus is placed in front of a large fan, which blows air along one of the arms at 8 m/s. Estimate the frequency of the beats that occur because of the interference of the waves reflected along the two arms of the interferometer. (hint: Be careful! You are measuring the Doppler shift for sound for the case of a moving medium, and both the speed and wavelength change.)

2. Relevant equations
f' = fgamma[1 - cos(θ)(v/c)]
f' / f = (1 + v/c) / (√(1-(v/c)2))
u' = (u-v) / (1 - (v/c2)u)
These are all the equations in the corresponding section.

3. The attempt at a solution
Honestly, no idea where to start since I don't understand how these components are being put together, but I'm willing to bet that we need to find the relative velocity of the sound wave in the moving air medium. From there, we can make θ = 0 if they are moving apart or ∏ if they're moving together. At that point, you can find the adjusted frequency of the wave, but again, the equations will change depending on which way the sound and air are moving relative to each other (i.e. if the sound source is moving against, with, or perpendicular to the air.)