Wave intensity diminishes as the distance from the source increases, a phenomenon that adheres to the inverse square law.

To elaborate, wave intensity is defined as the power transmitted per unit area, with the area measured perpendicular to the wave’s direction of propagation. It is commonly expressed in watts per square meter ($\text{W/m}^2$). The intensity of a wave is directly proportional to the square of its amplitude. This implies that if the amplitude of the wave doubles, the intensity increases by a factor of four.

The relationship between wave intensity and distance is dictated by the inverse square law. According to this law, the intensity of a wave is inversely proportional to the square of the distance from the source. In simpler terms, as the distance from the wave source increases, the intensity of the wave decreases. For instance, if the distance from the wave source is doubled, the intensity drops to one-quarter of its original value.

This decrease in intensity is due to the fact that as a wave radiates outward from a source, it spreads over an increasingly larger area. Consequently, the power of the wave is distributed over this larger area, leading to a reduction in intensity.

This principle applies to all types of waves, including light waves, sound waves, and electromagnetic waves. For example, the farther you are from a light source, the less intense the illumination appears. Likewise, as you move away from a sound source, the volume of the sound diminishes. This reduction in intensity occurs because the energy of the light or sound wave is dispersed over a greater area.

In conclusion, wave intensity decreases as the distance from the source increases, in accordance with the inverse square law. This fundamental principle in wave physics is essential for understanding various phenomena, such as the perceived loudness of sounds and the brightness of light.