Detecting multi-path propagation when one acoustic signal is dominant
It seems to me that, in the conditions you describe, the most you will see is flat fading. One indication that flat fading is occuring is that a change in the positions of transmitter and receiver, and/or the reflectors causing the multipath, produce a significant change in the received power. Usually the change has to be of the order of $\lambda/2$ meters, so this may be unfeasible in your case.