Question

Refer to Interactive Solution 17.9 to review a method by which this problem can be solved. Two loudspeakers on a concert stage are vibrating in phase. A listener is 47.4 m from the left speaker and 34.1 m from the right one. The listener can respond to all frequencies from 20 to 20 000 Hz, and the speed of sound is 343 m/s. What is the lowest frequency that can be heard loudly due to constructive interference?

Answer 1

or constructive interference to occur then difference in the path lengths traveled by the sound waves from the speakers to the listener should be integral multiples of wavelengths

Then Δx = nλ

         x2 -x1 =nλ

        47.4 m 34.1 m= nλ

      13.3 m = nλ

  λ = 13.3/n

v = f*λ

f = v/λ = 343/ (13.3/n) = 343*n/13.3

n= 1

f= 343*1/13.3=25.7894737 Hz  

n = 2

f = 343*2/13.3 =51.5789474

so   two lowest frequencies that can be heard loudly due to constructive interference are

25.7894737 Hz   and

51.5789474 Hz