Yes, the inverse square law is based on the concept of a spherical wave.
The inverse square law describes the relationship between the intensity of a wave and the distance from the source. According to this law, the intensity of a wave decreases with the square of the distance from the source.
When a wave propagates from a point source, it spreads out in a spherical manner. The energy carried by the wave is distributed over the surface area of a sphere centered on the source. As the distance from the source increases, the same amount of energy is spread over a larger area.
The surface area of a sphere is proportional to the square of its radius. Therefore, as the distance from the source doubles, the same energy is spread over four times the area. This results in a decrease in intensity, or energy per unit area, according to the inverse square relationship.
Mathematically, the inverse square law can be expressed as:
I = (P / 4πr²),
where I is the intensity of the wave, P is the power of the source, and r is the distance from the source. The 4π term represents the surface area of a sphere, and the denominator r² reflects the spreading of the wave over that area.
Thus, the inverse square law is a consequence of the spherical spreading of waves from a point source.