In the case of a stone thrown into a quiet pool of water, the waves that propagate outward from the impact point are known as circular or spherical waves. The amplitude of these waves falls off with distance 'r' from the impact point according to the inverse square law.
The inverse square law states that the amplitude of a wave decreases in proportion to the square of the distance from the source. Mathematically, this relationship can be expressed as:
Amplitude ∝ 1/r²
This means that as the distance 'r' from the impact point increases, the amplitude of the waves decreases rapidly. The rate of decrease is inversely proportional to the square of the distance.
It's important to note that in real-world situations, factors like fluid friction and energy dissipation can affect the precise behavior of waves in water. However, in the absence of these factors, the inverse square law provides a general description of how the amplitude of waves decreases with distance from the source.