Two identical speakers emit sound waves of frequency `680 H_(Z)` uniformly in all directions with a total audio output of `1 mW` each. The speed of sound in air is `340 m//s`. A point `P` is a distance `2.00 m` from one speaker and `3.00 m` from the other.
(a) Finf the intensity `I_(1)` and `I_(2)` from rach speaker at point `p` separately.
(b) If the speakers are driven coherently and in phase, what is the intensity at point `p`?
(c ) If they driven coherently but of phase by `180^(@)`, what is the intensity at point `P`?
(d) If the speakers are incoherent, what is the intensity at point `p`?

Answer

A, B, C, D

Explanation

(a) `I = (P)/(4 pi r^(2))`
:. `I_(1) = (1 xx 10^(-3))/(4 pi (2)^(2)) = 19.9 xx 10^(-6) W//m^(2)`
`= 19.9 mu W//m^(2)`
`I_(2) = (1 xx 10^(-3))/(4 pi (3)^(2)) = 8.84 xx 10^(-6) W//m^(2)`
`= 8.84 mu W//m^(2)`
(b) `I_(p) = I_(max) = (sqrt(I_(1)) + sqrt(I_(2)))^(2)`
`= 55.3 mu W//m^(2)`
(c ) `I_(p) = I_(min) = (sqrt(I_(1)) - sqrt(I_(2)))^(2)`
`= 2.2 mu W//m^(2)`
(d) `I_(p) = I_(1) + I_(2)`
`= 28.7 mu W//m^(2)`