by what factor will the amplitude of the sound change?

Question

An audio speaker producing a steady sound at an outdoor concert is 36 ft away from you. If you move to a position where the speaker is 74 ft distant, by what factor will the amplitude of the sound change?

Answer 1

Sound amplitude is inversely proportional to the square of the distance from the source.

So. we can write A ₁= K/ d₁² where K is some constant and d₁ = 36. K then can be set equal to A₁ x d₁².

Correspondingly, A₂ = K / 74^2. Substituting K = A₁ x d₁² into the A₂ equation gives A₂ = A₁ x 36² / 74², so

A₂ / A₁ = 0.24