Intensity & Amplitude | CAIE 9702 Paper 1 Notes

Chapters

Paper 1

Physics9702

Intensity & Amplitude

Intensity is the power a wave delivers per unit area. It is how we measure “how much” a wave carries.

Louder sound and brighter light mean higher intensity, and intensity depends on the square of the amplitude.

Intensity: power spread over an area

Definition

2 marks

What is meant by wave intensity?

Model answer: The power transmitted per unit area normal to the direction of wave travel.

I = \dfrac{P}{A}

Symbols

$I$ = intensity (W m⁻²)
$P$ = power carried by the wave (W)
$A$ = area the power passes through, at right angles to the wave (m²)

A wave from a small source spreads over a bigger and bigger area as it travels, so the power per unit area gets smaller and the intensity decreases.
For an isotropic point source with negligible absorption, the wave spreads over a sphere of area $4\pi r^2$ , so $I \propto 1/r^2$ : double the distance, quarter the intensity.

Light from a small source spreads through a narrow near square and a much larger far square. — With negligible absorption, the same emitted power is shared across a larger area farther from an isotropic point source.

Intensity depends on amplitude squared

Intensity is proportional to the square of the amplitude: $I \propto A^2$ .
So doubling the amplitude does not double the intensity; it makes it four times as big.

Worked example

Doubling the amplitude

A wave's amplitude is doubled while nothing else changes. What happens to its intensity?

$I \propto A^2$ , so $\dfrac{I_2}{I_1} = \left(\dfrac{A_2}{A_1}\right)^2 = 2^2 = 4$ .

Answer

I \text{ becomes } 4\times \text{ larger}

Common mistake

It is amplitude squared, not amplitude. Trebling the amplitude multiplies the intensity by 9, not 3.

Your turn9702/22/M/J/25 Q3(d)

Wave X has amplitude 10 cm and wave Y has amplitude 20 cm. Find $I_X/I_Y$ . (9702/22/M/J/25 Q3(d))

Show worked answer

Answer

\dfrac{I_X}{I_Y}=\left(\dfrac{10}{20}\right)^2=0.25

Intensity & Amplitude

Intensity is the power a wave delivers per unit area. It is how we measure “how much” a wave carries.

Louder sound and brighter light mean higher intensity, and intensity depends on the square of the amplitude.

Intensity: power spread over an area

Definition

2 marks

What is meant by wave intensity?

Model answer: The power transmitted per unit area normal to the direction of wave travel.

I = \dfrac{P}{A}

Symbols

$I$ = intensity (W m⁻²)
$P$ = power carried by the wave (W)
$A$ = area the power passes through, at right angles to the wave (m²)

A wave from a small source spreads over a bigger and bigger area as it travels, so the power per unit area gets smaller and the intensity decreases.
For an isotropic point source with negligible absorption, the wave spreads over a sphere of area $4\pi r^2$ , so $I \propto 1/r^2$ : double the distance, quarter the intensity.

Intensity depends on amplitude squared

Intensity is proportional to the square of the amplitude: $I \propto A^2$ .
So doubling the amplitude does not double the intensity; it makes it four times as big.

Worked example

Doubling the amplitude

A wave's amplitude is doubled while nothing else changes. What happens to its intensity?

$I \propto A^2$ , so $\dfrac{I_2}{I_1} = \left(\dfrac{A_2}{A_1}\right)^2 = 2^2 = 4$ .

Answer

I \text{ becomes } 4\times \text{ larger}

Common mistake

It is amplitude squared, not amplitude. Trebling the amplitude multiplies the intensity by 9, not 3.

Your turn9702/22/M/J/25 Q3(d)

Wave X has amplitude 10 cm and wave Y has amplitude 20 cm. Find $I_X/I_Y$ . (9702/22/M/J/25 Q3(d))

Show worked answer

Answer

\dfrac{I_X}{I_Y}=\left(\dfrac{10}{20}\right)^2=0.25