A bir is singing on a tree and a man is hearing at a distance `r` from the bird. Calculate the displacement of the man towards the bird so that the loudness heard by man increases by `20dB`. [Assume that the motion of man is along the joining the bird and the man].

Options

A. `(3r)/(4)`
B. `(3r)/(10)`
C. `(2r)/(3)`
D. `(9r)/(10)`

Answer

D

Explanation

Loudness `beta=10log_(10).(I)/(I_0)`
`:. beta_2-beta_1=10log_(10).(I_2)/(I_1)` and `I=(P)/(4pir^2)`
`:. (I_2)/(I_1)=(r_1^2)/(r_2^2)`
`:. (beta+20)-beta=10log_(10).(r^2)/(r_2^2)=20log_(10).(r )/(r_2)`
`implies(r )/(r_2)=10impliesr_2=0.1r`
`:.` Shift `=r-0.1r=0.9r=(9r)/(10)`