Two sound sources are coherent and in phase. Is there constructive or destructive interference at the midpoint between the speakers?
Generally, there is constructive interference whenever the path-length difference is an integer times the wavelength.
The Attempt at a Solution
At the midpoint between the speakers, the path-length difference is zero, which corresponds to constructive interference.
However, can we apply the usual conditions for constructive and destructive interference to points between the speakers? Sound is a longitudinal wave. Consider the midpoint between the speakers and apply the superposition principle. At the midpoint, away from one speaker is toward the other. Thus, at a given time at this point, if the molecular motion due to one speaker is in one direction, the molecular motion due to the other will be in the opposite direction. Do we not, then, have destructive interference at the midpoint?