Question

Interference with Loudspeakers

Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves OUT of phase. The frequency of the waves emitted by each speaker is 172 Hz. You are 8.00 m from speaker A. Take the speed of sound in air to be 344 m/s.(Hint: out of phase means their phase constants differ by pi )

(a) What is the closest you can be to speaker B and be at a point of maximum constructive interference?

(b) What is the SECOND closest distance speaker B can be from speaker A where you hear nothing?

Answer 1

a) condition for constructive interference= delta L = n $\lambda$ + $\lambda$ /2

let the distance between two speakers = x

path difference= sqroot ( x^2+ 64) - 8 = $\lambda$ /2

sqroot ( x^2+ 64) = $\lambda$ /2 + 8

$\lambda$ = c/v= 344/ 172= 2 m

sqroot ( x^2+ 64) =9

x^2+ 64= 81

x= 4.123 m

closest disatnce between speaker B and max interfernce= sqroot (x^2+ 64) = 9m

b) destructive interference

delta L = $\lambda$ + $\lambda$ /2= 3 m

sqroot ( x^2+ 64) - 8 = 3

x^2+ 64= 121

x= 7.55 m apprx