A Michelson interferometer for sound waves is made with a lo

A Michelson interferometer for sound waves is made with a loudspeaker as source, a microphone as detector, a thin sheet of paper as beam splitter, and two pieces of board as mirrors (see the figure). The arms of the interferometer are of equal length l, and the whole apparatus can be rotated. A wind, constant in speed and direction, blows past the apparatus. Once every second the speaker emits a very brief pulse of sound. Answer the following questions, using the result of Problem 2-8. In most orientations of the interferometer the echo received by the microphone consists of two pulses in quick succession. Why? At certain orientations of the interferometer the time delay between the two echoes is maximum. How many such orientations are there in one complete revolution of the apparatus? In relation to the direction of the wind, what are these orientations? If the length of each arm of the interferometer is 3 m, and the maximum time delay between echoes is found to be 10^-5 sec, what is the speed of the wind? Sound waves travel with a constant velocity relative to the air. Take the magnitude of this velocity to be 300 m/sec.

Solution

a) The sound ray reflected from the mirror M1 travels through the card board only once, where as the sound ray travels reflected from M2 must pass twice . thisis the reason two impulses will be heard in sucession.

b) At Cos(theta) =0, Pie/2 , time delay will be maximum

c) 4.48m/s