Question

Two loudspeakers are 1.50 m apart. A person stands 3.00 m from one speaker and 3.60 m from the other.

a) What is the lowest frequency at which destructive interference will occur at this point if the speakers are in phase?

b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 degrees Celsius.

Answer 1

Given that

distance between speakers, d = 1.50 m

distance between a person and 1st speaker, x₁ = 3.00 m

distance between a person and 2nd speaker, x₂ = 3.60 m

a) the path difference between the waves dut to two persons is given by

x₂ – x₁ = 3.60 – 3.00 = 0.60 m

from destructive interference, we have

x₂ – x₁ = (2n + 1)lambda/2 = 0.60 m

for the lowest frequency and hence the wavelength, n=0

we get

x₂ – x₁ = lambda/2 = 0.60 m

lambda = 1.20 m

The frequency is related to wavelength as

f = v/lambda

where, v = speed of sound in air = 343 m/s