---
title: "Intensity: the Energy and Power Carried by a Wave"
description: "A wave carries power proportional to the square of its amplitude, and intensity is that power spread over area. Spreading in three dimensions is why intensity falls with the square of the distance."
canonical: https://lightmysky.com/learn/science/intensity-the-energy-and-power-carried-by-a-wave-mt_Hj-yG6g3CD
source: https://lightmysky.com/learn/science/intensity-the-energy-and-power-carried-by-a-wave-mt_Hj-yG6g3CD.md
retrieved: 2026-09-12
---

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# Intensity: the Energy and Power Carried by a Wave

A wave carries power proportional to the square of its amplitude, and intensity is that power spread over area. Spreading in three dimensions is why intensity falls with the square of the distance.

Subject: Science · Area: Waves, Light & Sound · Ages 18 to 19
Page: https://lightmysky.com/learn/science/intensity-the-energy-and-power-carried-by-a-wave-mt_Hj-yG6g3CD

## Ready when they can

- Relates the power carried by a wave to its amplitude and frequency
- Applies the inverse square law to a source radiating into space
- Converts between intensity and the decibel scale for sound

## Lesson: How waves fade with distance

For a string or sound wave, power grows as the square of amplitude times the square of frequency. Double the amplitude and power quadruples. Intensity is that power spread over area, measured in watts per square metre.

A siren pours out fixed power that spreads over an ever growing sphere. Intensity therefore falls as one over distance squared. Double the distance and the intensity drops to a quarter.

**Example.** Stand twice as far from a siren and each patch of air gets one quarter of the power, with no absorption needed. The sound fades because the same power spreads thin.

Sound loudness uses decibels: a rise of 10 dB means ten times the intensity. Two such rises in a row mean one hundred times.

**Recap.** Power follows amplitude squared times frequency squared, and distance spreads it over one over r squared.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Wave Speed on a String from Tension and Linear Density](https://lightmysky.com/learn/science/wave-speed-on-a-string-from-tension-and-linear-density-mt_83x7vwb7UU)
- [Progressive Waves: Phase and Path Difference](https://lightmysky.com/learn/science/progressive-waves-phase-and-path-difference-mt_RotpycCNF8)

## Opens up

- [Flux, Magnitudes and the Distance Ladder](https://lightmysky.com/learn/science/flux-magnitudes-and-the-distance-ladder-mt_q1vEUas3AY)