The ratio of the amplitude of sound waves at different distances from a point source depends on the inverse square law. According to the inverse square law, the intensity of sound decreases with the square of the distance from the source.
Mathematically, the inverse square law can be expressed as:
I ∝ 1/r²
Where: I is the sound intensity, which is directly proportional to the square of the amplitude. r is the distance from the source.
If we consider two distances, r₁ and r₂ (where r₁ > r₂), and their corresponding amplitudes A₁ and A₂, the ratio of the amplitudes can be determined as follows:
(A₁/A₂)² = (I₁/I₂) = (r₂/r₁)²
Therefore, the ratio of the amplitudes of sound waves at two different distances from a point source is equal to the square root of the ratio of their distances from the source.