Question

Loudness of sound from an isotropic point source at a distace of `70cm` is `20dB`. What is the distance (in m) at which it is not heard.

Answer 1

Intensity from a point source varies with distance as `Iprop(1)/(r^2)`
Let at distace `r_1=10m` Intensity is `I_1`
Then given `20=10log((I_1)/(I_0))` .(i)
let for `r=r_2`, sound level be zero. Then intensity at that point should be `I_2=I_0`
And `(I_1)/(I_2)=((r_2)/(r_1))^2implies(I_1)/(I_0)=((r_2)/(r_1))^2` .(ii)
From Eqs. (i) and (ii) we get
`20=10log((r_2)/(r_1))^2implies20=20log((r_2)/(r_1))`
`implies(r_2)/(r_1)=10impliesr_2=10r_1=7m`