3.14PH1 · Section 3: Waves

Properties of waves

Key learnings

Transverse vs longitudinal waves
Transverse wave: the oscillation is perpendicular to the direction of travel and energy transfer. Examples: all electromagnetic (EM) waves (light, radio, microwaves, IR, UV, X-rays, gamma), water surface waves. Longitudinal wave: the oscillation is parallel to the direction of travel, forming compressions and rarefactions. Example: sound in air. Both transfer energy without permanently moving the matter they pass through (spec 3.4).
Wave properties + v = fλ, f = 1/T
Amplitude ( $A$ ): maximum displacement from the equilibrium position; metre (m). Wavelength ( $\lambda$ ): crest-to-crest distance; metre (m). Frequency ( $f$ ): complete waves passing a point per second; hertz (Hz). Period ( $T$ ): time for one cycle; second (s). Wavefront: a line joining points in phase. Formulae: $v = f\lambda$ (m/s) and $f = 1/T$ — both on the formula sheet. Mini-example: $f = 5$ Hz, $\lambda = 2$ m → $v = 10$ m/s.
Doppler, reflection, refraction
Doppler effect (3.8): a source moving TOWARDS you gives a higher frequency (shorter λ); moving AWAY, lower (longer λ) — the wave speed is unchanged. Reflection (3.9): all waves reflect with angle of incidence = angle of reflection, measured from the normal. Refraction (3.9): waves change direction and wavelength when the wave speed changes between media, but the frequency stays constant. Entering a denser medium, speed and wavelength both fall.

Common mistakes

Drawn from real examiner reports.

Wave type needs "relative to travel"

The definition needs two elements: the direction of oscillation, stated relative to the direction of travel. "Transverse waves vibrate up and down" is wrong — it omits the reference and only holds horizontally. Correct: transverse = oscillation perpendicular to travel; longitudinal = parallel to travel. Do not call sound transverse (it is longitudinal) or light longitudinal.

June 2024 Paper 2P Q5 -- candidates who described wave type without referencing the direction of travel relative to the direction of oscillation lost the definition mark.

Amplitude vs wavelength on a diagram

On a displacement-distance graph, amplitude is the vertical distance from the equilibrium line to a crest — NOT crest to trough, which is twice the amplitude. Wavelength is the horizontal crest-to-crest distance. Both are in metres but measure different things: amplitude is how tall, wavelength is how wide one cycle is. Reading crest-to-trough doubles the amplitude.

Not converting ms to seconds

Period $T$ must be in seconds before $f = 1/T$ . A period of 2.0 ms is $2.0 \times 10^{-3}$ s, so $f = 1/(2.0 \times 10^{-3}) = 500$ Hz — not 0.5 Hz (unconverted). Never read "ms" as minutes: milliseconds are thousandths of a second. Convert ms → s (÷1000) first, then take the reciprocal.

June 2024 Paper 2P Q5(c)(i) -- some candidates gave incorrect frequency by not converting the period from milliseconds to seconds correctly. November 2024 Paper 2P general comments -- incorrect ms-to-s conversion was a recurring error across wave calculations.

Echo: forgetting to halve the distance

In echo/sonar questions the pulse travels TO the surface AND back, so $vt$ is the TOTAL path — the depth or distance is $vt/2$ . Example: an echo after 0.24 s at 1500 m/s gives $d = 1500 × 0.24 = 360$ m total, so depth $= 360/2 = 180$ m. Giving 360 m (not halving) is the classic error; doubling when the one-way time is given is the reverse trap.

Refraction: frequency stays constant

When a wave refracts (enters a new medium) its frequency does not change — only the wave speed and wavelength change. Entering a denser medium, speed and wavelength both DECREASE while $f$ stays the same, consistent with $v = f\lambda$ . Writing that the frequency changes on refraction is a common error; the source sets the frequency, not the medium.

Doppler: wave speed does not change

In the Doppler effect it is the OBSERVED frequency and wavelength that change when the source moves — the wave speed stays the same, set by the medium. A source approaching bunches the wavefronts, shortening the observed wavelength and raising the pitch; receding does the reverse. Do not say the wave "speeds up" as the source approaches.

Exam tips

"Show that": write every step
The answer is given, so the marks are for METHOD. For a period/frequency "show that": (1) state $f = 1/T$ ; (2) substitute with units converted ( $T = 2.0 \times 10^{-3}$ s); (3) evaluate ( $f = 500$ Hz); (4) conclude. Writing only " $f = 500$ Hz" with no working scores zero.
Oscilloscope trace: constant period
On an oscilloscope-trace question every cycle must span the SAME number of squares — the period must be constant across the whole trace. A trace where the period drifts scores zero even if one cycle is drawn correctly. Keep the squares per cycle identical.
v = fλ: convert units, then substitute
For $v = f\lambda$ (or $f = 1/T$ ), first put quantities in base units: wavelength in metres, frequency in Hz, time in seconds (ms → s ÷1000). Then substitute and add the unit (m/s for speed, Hz for frequency). Rearrange for the unknown: $\lambda = v/f$ , $f = v/\lambda$ .
Doppler: use the wavefront chain
For "explain why the pitch rises as a source approaches", give the chain: source moves towards you → wavefronts bunch up → observed wavelength shorter → by $v = f\lambda$ with $v$ fixed, $f$ is higher → higher pitch. Reverse for a receding source; the wave speed is unchanged.

Revision notes