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Consider ten identical sources of sound....

Consider ten identical sources of sound. All giving the same frequency but having phase angles which are random.If the average intensity of each source is ` I_0 ` the average of resultant intensity I due to all these ten sources will be

A

`I = 100 I_(0)`

B

`I = 10 I_(0)`

C

`I = I_(0)`

D

`I = sqrt(10) I_(0)`

Text Solution

Verified by Experts

The correct Answer is:
B
In case of interference of two waves resultant intensity is give as
`I_(R) = I_(1) + I_(2) + 2 2sqrt(I_(1)I_(2)) cos phi`
If `phi` varies randmoly with time, so `(cosphi)_(av) = 0`
`I = I_(1) + I_(2)`
For n indentical waves, `I = I_(0) + I_(0) + ... = nI_(0) here I = 10I_(0)`
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