Question

Two speakers, one directly behind the other, are each generating a 240-Hz sound wave. What is the smallest separation distance between the speakers that will produce destructive interference at a listener standing in front of them?

Answer 1

Answer:

Explanation:

frequency, f = 240 hz

speed of sound, v = 343 m/s

Let λ is the wavelength.

v = f x λ

343 = 240 x λ

λ = 1.43 m

The smallest separation for the destructive interference is given by

d = λ / 2

d = 1.43 / 2 = 0.71 m

Answer 2

Answer:

The smallest separation distance between the speakers is 0.71 m.

Explanation:

Given that,

Two speakers, one directly behind the other, are each generating a 240-Hz sound wave, f = 240 Hz

Let the speed of sound is 343 m/s in air. The speed of sound is given by the formula as :

$v=f\lambda\\\\\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{343\ m/s}{240\ Hz}\\\\\lambda=1.42\ m$

To produce destructive interference at a listener standing in front of them,

$d=\dfrac{\lambda}{2}\\\\d=\dfrac{1.42}{2}\\\\d=0.71\ m$

So, the smallest separation distance between the speakers is 0.71 m. Hence, this is the required solution.