Two in-phase speakers are 2.8 m apart and emit an unknown single frequency of so

Question

Two in-phase speakers are 2.8 m apart and emit an unknown single frequency of sound. At a point 2.0 m away from one speaker on the line AB between the two speakers a sound detector records a sound intensity maximum. The detector is then moved perpendicularly away from the line AB. The first time the sound intensity is again measured to be a maximum occurs 1.5 m away from the line AB. What is the frequency of the sound? (Note: The path difference decreases as the detector is moved away from the line AB. Also, you must not assume n=1 a priori for either position.)

Explanation / Answer

since the difference between the distances is 0.8 m in the final situation and this is the next maximum just after maximum at 1.2 m path difference we know (n+1)*k/2 = 1.2-------------------------------first case and n*k/2 = 0.8--------------------------------second case where k = wavelength of the wave. => k/2 = 0.4 => k = 0.8 m => frequency is f = 343.2/0.8 = 429 Hz ( where 343.2 is the velocity of sound in air,, because it was not specified i had to assume it)

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