A person is standing at a distance D from an isotropic point source of sound He walks 50.0 m towards the source and observes that the intensity of the sound has doubled. His initial distance D from the source is

Options

A. `50sqrt2m`
B. `(50sqrt2)/(sqrt2-1)m`
C. `(50)/(sqrt2-1)m`
D. `100sqrt2m`

Answer

B

Explanation

Using `(P)/(4piR^2)=I`
`implies((P)/(4pi(D-50)^2))/((P)/(4piD^2))=(2)/(1)implies(D^2)/((D-50)^2)=2`
`rArr D=sqrt2(D-50)implies(sqrt2-1)D=20sqrt2`
`impliesD=(50sqrt2)/(sqrt2-1)=170.7m`