Two loudspeakers, A and B, are separated by a distance of 2.0 m. The speakers em

Question

Two loudspeakers, A and B, are separated by a distance of 2.0 m. The speakers emit sound waves at a frequency of 680 Hz that are exactly out of phase. The speed of sound is 343 m/s. How far from speaker A along the +x axis will a point of constructive interference occur?

A) 0.25 m

B) 0.30 m

C) 0.46 m

D) 0.88 m

E) 0.98 m

answer is D but idk how to derive it...i know you needf wave length which is .4852 and it needs to be a 1/2 integer since relation to wavelength since out of pase..thats where im stuck

Explanation / Answer

the path length difference is an odd-integer multiple of 1/2 wavelength. This, together with the initial 1/2 wavelength phase difference between emitted sounds, will result in an integer multiple of wavelengths path differense and thus constructive interference or reinforcement. Two such points are 1/4 wavelength to either side of the midpoint between A and B.
Approximate the wavelength as 0.5 m. Then reinforcement points are at 0.875 m and 1.125 m from A. One path length is 1.75 wavelengths and the other is 2.25 wavelengths

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