Two loudspeakers 5m apart, are calibrated to emit sound waves in phase within a

Question

Two loudspeakers 5m apart, are calibrated to emit sound waves in phase within a narrow frequency range of 500 Hz - 700 Hz. If you stand directly in front of one of the speakers 7 m away. you notice that the intensity of the sound waves deaching you is at a minimum.

what's the frequency  of the sound waves emitted by the speakers? ( the speed of sound in air 340 m/s)

Please, show me the steps

Two loudspeakers 5m apart, are calibrated to emit sound waves in phase within a narrow frequency range of 500 Hz - 700 Hz. If you stand directly in front of one of the speakers 7 m away. you notice that the intensity of the sound waves deaching you is at a minimum. what's the frequency of the sound waves emitted by the speakers? ( the speed of sound in air 340 m/s)

Explanation / Answer

for minimum friquency r2-r1 = (n+1/2)wavelength

r2 = sqrt(7^2+5^2)= 8.6 m

wavelength = v/f

= 340/f

so

8.6-7 = (n+1/2)*340/f

f = (n+1/2)*340/(1.6)

= (n+1/2)*212.5

now

frequency range is 500 Hz - 700 Hz.

so n= 2

f= 531.25 hz

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