Question

Sounds from two identical sources S1 and S2 reach a point P. When the sounds reach directly, and in the same phase, the intensity at P is I0. The power of S1 is now reduced by 64 %, and the phase difference between S1 and S2 is varied continuously. The maximum and minimum intensities recorded at P are now Imax and Imin.

(a) Imax = 0.64 I0

(b) Imin = 0.36 I0

(c) Imax /Imin = 16

(d) Imax /Imin = 1.64/0.36

Answer 1

Correct Answer is: (a) Imax = 0.64 I0 , (c) Imax /Imin = 16

Let a = initial amplitude due to S1 and S2 each.

I0 = k(4a2), where k is a constant.

After reduction of power of S1, amplitude due to S1 = 0.6a.

Due to superposition, amax = a + 0.6a = 1.6a, and

amin = a - 0.6a = 0.4a

Imax/Imin = (amax/amin)2 = (1.6a/0.4a) = 16.