P3.24SD0 · Section P3: Waves

Properties of waves

Key learnings

Wave quantities — amplitude, wavelength, frequency, period
Amplitude — maximum displacement of a point from its rest (equilibrium) position (m), NOT "the height of the wave". Wavelength ( $\lambda$ ) — distance between adjacent in-phase points, e.g. crest to crest (m). Frequency ( $f$ ) — complete waves passing a point per second (Hz), = $1/T$ . Period ( $T$ ) — time for one complete wave to pass a point (s). A wavefront joins points in phase. A wave transfers energy, not matter — particles only oscillate about a fixed point.
Wave equations: v = fλ and f = 1/T
The wave equation $v = f\lambda$ links wave speed $v$ (m/s), frequency $f$ (Hz) and wavelength $\lambda$ (m). The frequency-period relation $f = \dfrac{1}{T}$ links frequency $f$ (Hz) and period $T$ (s). Always write the equation, then substitute the data before rearranging to keep the substitution mark. Convert to SI first: 1 kHz = 1000 Hz, 1 MHz = $10^6$ Hz, cm to m. With standard-form data, check the power of ten.
Wave types, Doppler, reflection and refraction
In a transverse wave the oscillations are perpendicular to the energy-transfer direction (EM waves, water ripples); in a longitudinal wave they are parallel, giving compressions and rarefactions (sound). Doppler effect: as a source approaches, wavefronts bunch up, so observed wavelength decreases and — since $v = f\lambda$ ( $v$ constant) — frequency increases; moving away reverses it. All waves can also be reflected and refracted (direction changes as speed changes).

Common mistakes

Drawn from real examiner reports.

Amplitude ≠ height of the wave

Amplitude is the maximum displacement from the equilibrium (rest) position — measured from the middle line to a crest. "The height of the wave" is not credited because it can be read as crest-to-trough, which is twice the amplitude. Amplitude is measured up from the midline, wavelength along the wave — never the same measurement.

Frequency is complete waves per second

Frequency must be stated as "the number of complete waves passing a point per second" (or $1/T$ ), not "how often a wave happens" or "how fast it vibrates". Its unit is the hertz (Hz), one complete wave per second — not the metre (that is wavelength) and not the second (that is the period). Vague wording loses the definition mark.

Comparing waves — say HOW they differ

When comparing two waves, "they have different frequencies/wavelengths" earns nothing — you must say how they differ (which one is higher). Nearly half of candidates lost every mark here, and weaker ones swapped the two terms: for a fixed wave speed frequency and wavelength are inversely related, so a higher frequency means a shorter wavelength.

June 2024 Paper 1P Q3(b)(ii)

Name the oscillations, not just the angle

To distinguish the wave types you must refer to the oscillations and the energy-transfer direction: transverse = oscillations perpendicular, longitudinal = parallel. Candidates who wrote only "perpendicular/parallel" without mentioning the oscillations, or who confused particle motion with wave direction, lost marks; any supporting diagram must be labelled.

November 2024 Paper 1P Q8(a); June 2023 Paper 1P Q6(a)(iii)

Doppler: the wave speed is constant

In a Doppler question the medium is unchanged, so the wave speed stays constant — it is the wavelength that changes as the wavefronts bunch or spread. Many wrongly said the speed changed, and many wrote "frequency increases" without quoting $v = f\lambda$ or noting the constant speed. The chain: $\lambda$ decreases $\rightarrow$ (with $v$ constant) $f$ increases.

November 2024 Paper 1P Q8(b)

Measure refraction angles from the normal

In refraction diagrams, always measure the angle of incidence and refraction from the normal (the line perpendicular to the surface), never from the surface itself. Only about a quarter of candidates drew the emerging ray bending in the correct direction — entering a denser medium the ray bends towards the normal, leaving it bends away.

November 2024 Paper 1P Q6(c)

Exam tips

Substitute before you rearrange
Write the equation ( $v = f\lambda$ or $f = 1/T$ ) — that alone can earn a mark — then substitute the data before rearranging. Candidates who rearranged first and slipped scored zero, while those who substituted first kept the method mark.
Convert to SI units first
Before substituting, convert to SI base units: kHz/MHz to Hz (1 MHz = $10^6$ Hz), cm to m, ms to s. The MHz $\rightarrow$ Hz conversion is the main failure in wave calculations, though not converting still allows a method mark for a correct rearrangement.
Check the power of ten
With standard-form data (e.g. $3 \times 10^8$ m/s), enter values carefully and sanity-check the exponent of your answer; marks are regularly lost to power-of-ten and rounding errors. Always state the unit with your final answer.

Revision notes