Question

Two loudspeakers on a concert stage are vibrating in phase. A listener 50.5 m from the left speaker and 26.0 m from the right one. the listener can respond to all frequencies from 20 to 20 000Hz, and the speed of sound is 343 m/s. What are the two lowest frequencies that can be heard loudly due to constructive interference?

Answer 1

for constructive interference to occur then difference in thepath lengths travelled by the sound waves from the speakers to thelistener should be integral multiples of wavelengths

Then Δx = nλ

         x2 -x1 =nλ

         50.5 m -26 m= nλ

       24.5 m = nλ

if n=1

Then λ1 = 24.5 m

Then velocity of sound is v = 343 m/s

Then frequency is f 1 = v/λ1 = 343/24.5 = 14Hz

if n=2

24.5 m = 2*λ2

Then λ2 = 12.25 m

Then frequency is f 2 = v/λ2 = 343/12.25 = 28 Hz

if n= 3

24.5 m = 3*λ2

Then λ2 = 8.167 m

Then frequency is f 2 = v/λ3= 343/8.167 = 42 Hz

the two lowest frequencies that can be heard loudly due toconstructive interference are 28Hz and 42Hz.