Intensity: power spread over an area

7 minAS Level7.1.7

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can calculate intensity from power and area, use the fact that intensity is proportional to amplitude squared, and explain why doubling the amplitude does not merely double the intensity.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$A_2$	second amplitude
$A_1$	first amplitude
$I_2$	second (or new) intensity
$I_1$	first (or original) intensity
$I_3$	third intensity

The same power over a bigger area

A loudspeaker emits a fixed amount of sound energy every second. That is its power.

Stand close and the sound is loud; stand further away and it is quieter, even though the speaker has not changed. The same power is now spread over a larger area.

Intensity measures how concentrated that power is.

Definition

Intensity

The intensity of a wave is the power transmitted per unit area perpendicular to the direction of travel:

$I = \frac{P}{A}$

where $P$ is the power in watts and $A$ is the area in square metres.

The unit is therefore $\text{W m}^{-2}$ .

Intensity is a measure of how much energy arrives per second on each square metre, so it is closely related to loudness (for sound) and brightness (for light).

Worked example: Worked example: intensity from power and area

A small loudspeaker emits a total power of $2.0\ \text{W}$ , spread evenly over an area of $0.50\ \text{m}^2$ .

Calculate the intensity.

Have a go first?

Quick check

CalculateQuestion 1 · Recall

Multiple choiceQuestion 2 · Recall

Answer the 3 questions above to continue.