@mcnees I think that this is answer is incorrect.
Since your body and measuring equipment would be composed of sound waves, I think that whenever you measured the speed of sound, the speed of sound relative to you would always be 340 m/s from your perspective, regardless of your speed relative to the medium.
Imagine you're using "phonon clocks" to measure time passing, etc.
Since you, the observer, are made out of sound waves, your perceived measurement of time and distances would be altered.