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**

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