Question

17.
Two coherent sources are placed at the corners of a rectangular track of sides 3 m & 4 m. The source
S, lags S, by phase angle tt. A detector is moved along path ABC. Then find:
Position of detector where the phase difference between the sound waves of sources S, and 3, is
zero.
Find the ratio of total number of minima detected on line AB to the total number of minima on line BC,
[Velocity of sound = 330 m/s; Frequency of sources S, and S, - 165 Hz)​

Answer 1

Position of detector where the phase difference between the sound waves of sources S, and 3, is  zero is at B.

The ratio of total number of minima detected on line AB to the total number of minima on line BC is 2 : 3

Explanation:

(i) The phase angle is given by the formula:

θ = (ωt - kx)

The phase angle 's₁' is given by the formula:

θ₁ = (ωt - kx₁) → (equation 1)

The phase angle 's₂' is given by the formula:

θ₂ = (ωt - kx₂ + π) → (equation 2)

On equation equation (1) and (2), we get,

(ωt - kx₁) = (ωt - kx₂ + π)

kx₂ - kx₁ = π

Now,

V/n = λ = 330/165 = 2

2x₂ - 2x₁ = λ

x₂ - x₁ = 1

On the path ABC it is possible at B where x₂ = 4 and x₁ = 3

Thus, At B on ABC

(ii) Ratio:

At A, the phase difference is 4π and at B, the phase difference is zero. Thus, it will be π and 3π which is two minima.

At C, the phase difference is 6π and between B and C, the phase difference is 1π, 3π and 5π which is three minima.

Thus, the ratio is 2 : 3