Interference of Two Sound Waves: Phase Difference & Intensity

[alireza83]

Consider two loudspeakers (emitting sound waves of the same amplitude and wavelength of 15m) and an observer located in the x−y plane, with the two loudspeakers being at (2m, 0) and (−2m, 0), respectively, and the observer being at (0, 3m) initially.

(i) Suppose the intensity of the combined sound heard by the observer is same as that of the sound from each loudspeaker by itself. Determine the possible values of the inherent phase difference between the two sound waves.
(ii) The observer then moves along the x-direction to reach the point (2m, 3m). For each of the possible cases mentioned in part (i), determine whether the interference at this new location of the observer is maximum constructive or maximum destructive or something in-between.

 

[UMDstudent]

I'm working on the same question; I'm actually a little confused myself, however, let me show you what I've done so far and hopefully someone else can elaborate:

Part A : Using the formula : Phase Difference = 2pi*(deltaX/Wavelength) + PhaseDiffConstant.

: 2pi*(4meters/15meters) = 8pi/15. We know that deltaX - x2 - x1 = 4 meters between the two speakers. We are given the wavelength at the beginning (15)

Part B, I did somewhat of the same thing:

2pi * (2/15) = 4pi/15. The 2 for DeltaX came from making a right triangle and seeing that the distance of the observer and the other speakers was 5-3 = 2 meters (overall).
This leads me to believe that the interference is somewhat in-between constructive and destructive as constructive = integers and destructive is integers + 1/2 .

Does this look correct? I'm looking for guidance please :)

-UMDstudent