We all know the earth is surrounded by an atmosphere, and we know that it is the medium through which sound travels. If the Michelson and Morley experiment was modified to find sound’s medium would they have found it? Replace the interferometer’s light with a sound chirp and measure its reflected speed off of a sound board. Do this over the course of the year looking for variances in the sounds speed. Rotate the apparatus just like the rotating interferometer. Wouldn’t they have concluded that is speed constant and there is no medium. Note: I know sound’s speed does vary due to temperature and altitude, but it does not vary do to its direction through it’s medium.
If the M and M experiment was modified to find sound’s medium would they have found it?
The Michelson Morley experiment, modified for sound. Would have also obtained a null result if it were performed in still air all the time. Of course any slight breeze would have caused a signal and led to more investigations, undoubtedly eventually uncovering the air. But for the sake of discussing your question let’s assume completely still air at all times.
I know sound’s speed does vary due to temperature and altitude, but it does not vary do to its direction through it’s medium.
Note, this would be irrelevant. The Michelson Morley interferometer did not measure the speed of light, but rather the difference in the speed of light along the two paths. In other words, it measured the isotropy of the speed of light. A change in temperature would change the speed of sound, but it would still be isotropic and give a null result.
The Michelson Morley experiment only ruled out the then extant rigid aether concept. That concept had a lot to recommend it since it explained both why light was so fast and why it could be polarized. However, the experiment did not rule out dragged aether theories, which would predict a null result for the same reason that you have identified for sound.
Dragged aether theories were later ruled out by other experiments, such as Sagnac’s. And other experiments progressively showed support for relativity. At a minimum, the Michelson Morley experiment, the Ives and Stillwell experiment, and the Kennedy Thorndike experiment together are required to experimentally determine the Lorentz transform to within about 0.1%