How are wave intensity and distance related?

Wave intensity decreases as the distance from the source increases, following the inverse square law.

In more detail, wave intensity is the power transferred per unit area, where the area is taken perpendicular to the direction of the wave. It is often measured in watts per square metre (W/m²). The intensity of a wave is directly proportional to the square of its amplitude. This means that if the amplitude of the wave doubles, the intensity of the wave increases by a factor of four.

The relationship between wave intensity and distance is governed by the inverse square law. This law states that the intensity of a wave is inversely proportional to the square of the distance from the source. In other words, as the distance from the source of the wave increases, the intensity of the wave decreases. For example, if the distance from the source of the wave doubles, the intensity of the wave decreases to a quarter of its original value.

This relationship is due to the fact that as a wave propagates outwards from a source, it spreads over a larger and larger area. As the area over which the wave spreads increases, the power of the wave is spread over a larger area, resulting in a decrease in intensity.

This principle is applicable to all types of waves, including light waves, sound waves, and electromagnetic waves. For instance, the further you are from a light source, the less intense the light appears. Similarly, the further you are from a sound source, the less loud the sound appears. This is because the energy of the light or sound wave is spread over a larger area, resulting in a decrease in intensity.

In summary, the intensity of a wave decreases as the distance from the source of the wave increases, following the inverse square law. This is a fundamental principle in wave physics and is crucial for understanding phenomena such as the perceived loudness of sounds or the brightness of light.