Question

9. Two out of phase loudspeakers are some distance apart. A person stands 5.50 m from one speaker and 3.70 m from the other. What is the lowest acceptable frequency at which the person will hear destructive interference? The speed of sound in air is 346 m/s.

Answer 1

First we want to find out the path difference,

distnce from the person to one speaker = 5.50 m

distance from the other = 3.70 m

the longest wavelength is the shortest frequency, so the path difference will be the difference between the speakers,

d = 5.5 - 3.7 = 1.8 m

we know = V / f

therefore   = 346  / f

for destructive interference,

d = (2n +1 )    / 2

n is integer

giving the values of d and

1.8 = (2n +1 ) / 2 x 346  / f

f = (2n +1 ) / 2 x 346 /1.8

= (2n +1 ) x 96.111

lowest frequency is n = 1

f = 3 x 96.11

= 288.3333