Follow by the Michelson–Morley experiment, What happen if we use something that has a speed lower than light instead of light in Michelson–Morley experiment? How about the result?
The aim of the Michelson–Morley experiment was to measure how fast the aether is moving relative to Earth, and to do this you need some phenomenon that propagates as a disturbance in the aether. Light was the only phenomenon believed (incorrectly of course :-) to propagate as a disturbance in the aether. That's why light was used.
As dmckee says in his comment, if you use something like sound you aren't measuring the speed of the aether because sound propagates as disturbances in air not in the aether. Using sound would measure how fast the air is moving relative to your equipment. This would work fine, though there are easier ways to measure wind speed.
Interesting question. Mathematically the apparatus using the Vl (velocity of light) and Ve (velocity of the aether) can not prove anything except Vl+Ve (1st leg) Vl (2nd leg) + Vl (3rd leg) +Vl-Ve (4th leg) = 4Vl which really demonstrates nothing. it will only show a difference in the fringes when accelerated.
the apparatus can not get past the Doppler like condition of what goes in one dimension V+v also returns in the same dimension V-v.