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Two sounds sources of same frequency pro...

Two sounds sources of same frequency produce sound intensities `I_(0) and 4I_(0)` at a point `P` when used separately . Now , they are used together so that the sound waves from the reach `P` with a phase difference `phi`. Determine the resultant intensity at `P` for
(i) `phi = 0` (ii) `phi = 2 pi //3` (iii) `phi = pi`

Text Solution

Verified by Experts

We know that
`I = I_(1) + I_(2) + 2 sqrt( I_(1) I_(2)) cos phi`
Thus ,
(i) for `phi = 0 , I = I_(0) + 4I_(0) + 2 sqrt((I_(0)) ( 4 I_(0))) = 9 I_(0)`
(ii) for `phi = 0 , 2 pi //3 , I = I_(0) + 4I_(0) + 2 sqrt((I_(0)) ( 4 I_(0))) cos (2pi)/(3)`
(iii) For `phi = pi , I = I_(0) + 4 I_(0) + 2 sqrt((I_(0)) ( 4 I_(0))) cos pi or I = I_(0)`
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