A point source of sound emits a constant power with intensity inversely proportinal to the square of the distance from the source . By how many decible does the sound intensity level drops when you move from point `P_(1)` to `P_(2)` ? Distance of `P_(2)` from the source is two times the distance of source from `P_(1)` .

Answer

A, B, D

Explanation

we label the two points `1` and `2`, and we use the equation `beta = 10`log `(I)/(I_(0)) (dB)` twice. The difference in sound intensity level `beta_(2) -beta _(1)` is given by
`beta_(2) -beta_(1) = (10 dB)(log .I_(2)/(I_(0))- log .I_(1)/(I_(0)))`
`(10dB)[(log I_(2)-log I_(0)) - (log I_(1) - log I_(0))]`
`= (10 dB) log .I_(2)/(I_(1))`
Now, `Iprop (1)/(r^(2))rArr :. (I_(2))/(I_(1))= ((r_(1))/(r_(2)))^(2)= (1)/(4) as r_(2) = 2r_(1)`
:. `beta_(2)- beta_(1) = (10 dB) log ((1)/(4)) = - 6.0 dB`