A speaker emits 0.8 W of acoustic power. Assume that it behaves as a point source which emits uniformly in all direction. At distance will the intensity level be 85 dB?

Explanation

From equation we know that the intensity of waves from a point source decreases as the inverse square of the distance r, that is `I = (P)/(4 pi r^(2)) " ". . . (i)`
We must find the intensity corresponding to an 85 - dB sound level:
` 85 = 10 "log" (I)/(I_(0))`
Thus, log `(I//I_(0)) = 8 . 5`
or `I = 10^(-12) xx 10^(8.5) = 3 . 16 xx 10^(-4) W //m^(2) " ". . . (ii)`
Using (ii) in (i) we find
`r^(2) = (P)/(4 pi I)`
`((0 . 8 W))/(4(3 . 14)(3 . 16 xx 10^(-4) W//m^(2))) = 201 m^(2)`
Thus r = 14 . 1 m .
Where I is the intensity of the sound and `I_(0)` is a constant reference intensity `10^(-12)W//m^(2)` . The reference intensity represents roughly the minimum intensity that is just audible at intermediate frequencies.For `I = I_(0)` , the sound level `beta = 0 ` . Table shows the approximate sound levels of some of the sounds commonly encountered.