Intensity and distance from the source

For a point-like, isotropic light (or sound) source, that is one emitting equally in all directions, the total power $P$ is spread over a sphere whose radius grows the further away one goes. The same energy must cover an ever larger surface, so it becomes more “diluted”.

Since the surface area of a sphere is $4\pi r^2$, the intensity $I$ — the power per unit area — decreases as $1/r^2$: this is the famous inverse-square law.

Key formula

$\ev{I(r) = \dfrac{P}{4\pi r^2}}$

The practical meaning is stark: doubling the distance from the source does not halve the intensity, it reduces it to a quarter. This is why a lamp or a loudspeaker seems to fade so quickly as one moves away.

Collegamenti

Argomenti: Ottica · Onde Concetti: Intensità di un’onda

Esercizi collegati: Problema — Distanza massima di un tuono · Problema — Ranking delle potenze di quattro onde · Problema — Potenza acustica di una conversazione