Intensity of Waves
Simple Explanation
Intensity measures how much power a wave delivers per unit area — it tells you how 'concentrated' a wave's energy is at a given point, which is why the same total power can feel much stronger or weaker depending on how spread out it is.
Why Do We Need It?
Intensity explains why sounds and light get weaker with distance from their source, and is directly related to perceived loudness (for sound) and brightness (for light).
Formula
Wave Intensity
I = P / A
Intensity measures how concentrated a wave's power is, spreading the total power carried by the wave over the area it passes through.
- I
- — Intensity, in W/m²
- P
- — Power carried by the wave, in watts
- A
- — Area the power is spread over, in m²
When to use it: Use to compare how "strong" a wave is at different distances from its source, or to find the power delivered over a given area.
Worked Example
Finding wave intensity
A speaker emits 0.5 W of sound power, spread evenly over a spherical area of 10 m². Find the sound intensity.
Why Does This Work?
As a wave (sound or light) spreads out from a point source, its fixed total power is distributed over an ever-increasing area (for a spherical wave, the surface area of a sphere, which grows with the square of distance) — this is why intensity decreases sharply (following an inverse-square relationship) as distance from the source increases.
Real-Life Example
Why sound gets quieter farther from a speaker
Standing farther away from a loudspeaker makes the sound noticeably quieter.
The speaker's total sound power stays the same, but as you move farther away, that same power is spread over an increasingly large spherical area — reducing the intensity (and therefore the perceived loudness) reaching you.
Practice
A source emits 2 W of power spread over an area of 4 m². Find the intensity.
MediumCommon mistake
Confusing intensity with total power — intensity accounts for how the power is SPREAD OUT (per unit area); the same power delivered over a smaller area produces a much higher intensity than over a larger area.
Quick Review
- I = P/A measures power per unit area.
- Intensity decreases as a wave spreads over a larger area with distance from its source.
- Intensity relates directly to perceived loudness (sound) or brightness (light).