Question

Two loudspeakers on a concert stage are vibrating in phase. A listener is 47.0 m from the left speaker and 33.1 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

let f is the lowest frequency of the sound wave that can be heard.

use, v = lamda*f

==> lamda = v/f

for minimum f, lamda must be maximum

lamda_max = v/f_min

= 343/20

= 17.15

given

r1 = 47.0 m
r2 = 33.1 m

path diffrence for constaructive intereference,

r2 - r1 = n*lamda

47 - 33.1 = n*lamda

13.9 = n*lamda

lamda = 13.9/n

v/f = 13.9/n

343/f = 13.9/n

==> f = 343*n/13.9

f = n*24.676

for minmum value of n = f_min/24.676

= 20/24.676

= 0.8105

so minumum value of n = 1

f = 1*24.7

= 24.7 hz