Question

a bird sitting on a Tree a person approaches the tree and policies that the intensity has increased by 10 decimals find the ratio of initial and final separation between the man and the bird.

Answer 1

Given :

Change in intensity = 10dB

To find :

The ration of initial to final separation between the man and the bird

Solution:

• Let initially the distance between the man and the bird be r₁

      I₁ = P/4πr₁²

      I₂ =  P/4πr₂²

• The intensity is has been changed by 10dB

• 10 log (I₂/I₁)  - 10 log(I₁/I₀)  = 10

• log (I₂/I₁)  - log(I₁/I₀)  = 1

• log (I₂/I₁) = 1

• I₂/I₁ = 10

• r₁² / r₂² = 10

• r₁/r₂ = √10 : 1

The ratio of initial and final separation is √10 : 1