Question

Harry and Sally are sitting on opposite sides of a circus tent when an elephant trumpets a loud blast. If Harry experiences a sound intensity level of 74 dB and Sally experiences only 48 dB, what is the ratio of the distance between Sally and the elephant to the distance between Harry and the elephant?

Answer 1

Sound intensity level experienced by Harry = ₁ = 74 dB

Sound intensity reaching Harry = I₁

Distance of Harry from the elephant = R₁

Sound intensity level experienced by Sally = ₂ = 48 dB

Sound intensity reaching Sally = I₂

Distance of Sally from the elephant = R₂

I₁ = 2.512 x 10^-5 W/m²

I₂ = 6.31 x 10^-8 W/m²

The sound intensity is distributed evenly over a spherical distribution hence,

I₁(4R₁²) = I₂(4R₂²)

I₁R₁² = I₂R₂²

(2.512x10^-5)R₁² = (6.31x10^-8)R₂²

R₂/R₁ = 398.1

Ratio of distance between Sally and the elephant to the distance between Harry and the elephant = 398.1