Physics 9702 · Paper 1

Phase & Phase Difference

Phase tells you where a point is in its cycle: rising, at a crest, falling, and so on.
Phase difference is how far out of step two points are, measured as a fraction of a full cycle.

In step, or out of step

Reading phase difference straight off a wave. A and B are one whole wavelength apart, so they move in step: phase difference 0°. C and D are only a quarter of a wavelength apart: phase difference 90°.

One full cycle is 360° (or $2\pi$ radians). Phase difference is given as an angle.
Two points exactly one wavelength apart move together: phase difference 0° (or 360°). They are in phase.
Half a wavelength apart, they are exact opposites: phase difference 180°, called antiphase.
A quarter of a wavelength apart gives 90°.

\Delta\phi = \dfrac{d}{\lambda}\times 360^\circ

Symbols

$\Delta\phi$ = phase difference (degrees)
$d$ = distance between the two points (m)
$\lambda$ = wavelength (m)

The method: work in fractions of a wavelength, not in raw distance. A gap of $d$ is the fraction $d/\lambda$ of a cycle, and a cycle is 360°.

Working out a phase difference

Worked example

Phase difference between two points

A progressive wave has frequency 300 Hz and travels at 600 m s⁻¹. Find the phase difference between two points 0.50 m apart.

First the wavelength: $\lambda = \dfrac{v}{f} = \dfrac{600}{300} = 2.0\text{ m}$ .
The points are $\dfrac{0.50}{2.0} = \tfrac{1}{4}$ of a wavelength apart.
So $\Delta\phi = \tfrac{1}{4}\times 360^\circ = 90^\circ$ .

Answer

\Delta\phi = 90^\circ

(9702/12/F/M/25 Q25)

Common mistake

Do not put the raw distance into an angle. 0.50 m is not 0.50 of a cycle. Always divide by the wavelength first, then multiply by 360°.

Your turn— tap to reveal the worked answer (9702/11/M/J/25 Q26)

On a snapshot of a wave, which labelled point has a phase difference of 270° from point X? (9702/11/M/J/25 Q26)

Answer: the point three-quarters of a wavelength further on (270° = $\tfrac{3}{4}$ of a cycle).

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