Question

SOUND WAVES FROM A POINT SOURCE ARE PROPAGATING IN ALL DIRECTIONS. WHAT WILL BE THE RATIO OF AMPLITUDES AT DISTANCES OF 8 m TO
25 m FROM THE SOURCE?

Answer 1

The sound intensity (I) and amplitude (A) are related as

I = kA²

or

I₁/I₂ = A₁ ² / A₂ ² (1)

also the relation between sound intensity and distance is given as

I₁/I₂ = r₂ / r₁ (2)

now, we can combine (1) and (2) as

A₁ ² / A₂ ² = r₂ / r₁

where r2 = 25 m

r1 = 9 m

thus,

A₁ ² / A₂ ² = 25 / 9

so, the ratio of their amplitude would be

A ₁ / A ₂ = 5/3