Question

Two small forward-facing speakers are 2.50 m apart. They are both emitting, in phase with each other, a sound of frequency 1100 Hz in a room where the speed of sound is 344 m/s. A woman is standing opposite the midpoint between the speakers and is initially 35.0 m from the midpoint. As she slowly walks parallel to the line connecting the speakers, at what angle θ (relative to the centerline coming outward from the midpoint between the speakers) will she first hear no sound?

B) 3.6°

Answer 1

The speed of the sound is and the frequency of the sound is

Wavelength of the sound is

Let the woman walks 'x₁' m from the center line at point 'P' where she doesn't hear any sound.

Since the two speakers emit sound of same wavelength, they mus interfere with each other and at point 'P', the intensity of the sound wave produce minima.

We know from 'Young's Double Slit' Experiment , the position of n^th  interference minima occurs at a distance from center line is given by

The woman reaches to first minima when n=1.

So we get

  

From geometry we find