Question

Two identical speakers, with the same phase constant, are arranged along a 1D track. One speaker remains at the origin. The other speaker can slide along the track to any position x. You are on the track at x=10 m. You hear interference maxima when the adjustable speaker's position is 0.6 m and 1.2 m and at no points in between. What is the frequency of the sound from the speakers in Hz?

Answer 1

Answer:

$f=571.67\ Hz$

Explanation:

Given:

• Two identical speakers have the same phase constant.

• One of the speaker remains origin.

• The other speaker moves linearly from origin to  x=10m

• position of maxima of the interference, $x_1=0.6\ m$

• position of next maxima of the interference, $x_2=1.2\ m$

Therefore we have the wavelength of the wave as the distance between the two consecutive maxima:

$\lambda=1.2-0.6$

$\lambda=0.6\ m$

We have the speed of sound in the air as:

$v=343\ m.s^{-1}$

Therefore the frequency of sound:

$f=\frac{v}{\lambda}$

$f=\frac{343}{0.6}$

$f=571.67\ Hz$