Waves transfer energy, not matter
A wave transfers energy from place to place without transferring matter: each part of the medium oscillates about a fixed position while the energy travels on. A crest is the highest point, a trough the lowest. Show wave motion three ways -- a rope flicked at one end; a slinky pushed along its length (longitudinal) or moved side to side (transverse); a ripple tank, where a vibrating bar makes water waves whose wavefronts can be measured.
Wave equation links speed, frequency and wavelength
For any wave , where is wave speed in m/s (distance a wavefront travels per unit time), is frequency in Hz -- the number of complete waves passing a point each second, not vaguely how often it happens -- and is wavelength in metres (m), the distance between adjacent points in phase, crest to crest. Rearranged: and . Amplitude is the maximum displacement from the rest position, measured centre line to crest.
(Extended) Transverse vs longitudinal, and diffraction
A transverse wave oscillates at right angles to the direction of energy transfer -- electromagnetic radiation, water waves, S-waves. A longitudinal wave oscillates parallel to it, travelling as compressions and rarefactions -- sound, P-waves. Diffraction is the spreading of a wave through a gap or round an edge: greatest when the gap is about one wavelength wide, least when it is far wider, and for a fixed gap a longer wavelength spreads more.
Drawn from real examiner reports.
Amplitude is not crest-to-trough
Amplitude is the maximum displacement from the rest (equilibrium) position -- centre line up to a crest. Crest-to-trough is twice the amplitude, so quoting it, or writing "amplitude = height of the wave", loses the mark. Draw the rest line first to measure from. A larger amplitude carries more energy, and for sound means a louder note -- never a quieter one.
Digest P3 -- loudness maps to amplitude, louder = GREATER amplitude, not quieter (Nov 2023 P13 Q34).
Wavelength is not crest-to-trough
Wavelength runs from one crest to the next crest -- or trough to trough, or between any two adjacent points in phase. Crest to the neighbouring trough is only half a wavelength, and marking it that way is the commonest labelling error on a wave diagram. Wavelength is a horizontal distance along the wave; amplitude is a vertical displacement.
kHz and MHz must become Hz first
Convert every prefix before substituting into . A frequency of 2 kHz is 2000 Hz; 500 MHz is Hz. Putting the bare 2 or 500 into the equation gives an answer wrong by a factor of a thousand or a million. Convert lengths in the same breath -- cm to m -- so that the speed comes out in m/s rather than a mixture of units.
Digest P3 bundle -- rearrange v = f x lambda, watch prefixes (MHz vs kHz), compute frequency before speed, read powers of ten off graph labels (Jun 2022 P41 Q6c; Jun 2023 P42 Q3cii; Nov 2023 P43 Q12iii).
Rearranging the wave equation upside down
To find frequency, divide: , speed over wavelength. To find wavelength, . Dividing the wrong pair -- -- returns a time (the period), not a frequency, and multiplying by gives neither. Then supply the unit: m/s for speed, Hz for frequency, m for wavelength. A bare number never scores the final mark.
Digest P3 bundle -- rearrange v = f x lambda, watch prefixes (MHz vs kHz), compute frequency before speed, read powers of ten off graph labels (Jun 2022 P41 Q6c; Jun 2023 P42 Q3cii; Nov 2023 P43 Q12iii).
A water wave is transverse
Water waves are transverse: the surface oscillates up and down while the wave travels horizontally. Labelling one longitudinal is a persistent error. Of the syllabus examples only sound and P-waves are longitudinal, travelling as compressions and rarefactions along the direction of travel; light (all electromagnetic radiation) and S-waves are transverse too.
Digest P3 bundle -- sound is longitudinal (compressions/rarefactions) while a water wave is transverse, though many say longitudinal (Jun 2023 P43 Q3cii; Nov 2022 P42 Q6bi).
A wave does not carry matter along
When a wave passes, the particles of the medium oscillate about fixed positions and go nowhere on average -- only energy moves forward. A cork floating on ripples bobs up and down on the spot; it is not swept across the tank. Answers such as "the water moves across" or "the particles travel with the wave" describe a current, not a wave, and score nothing.
Reflection vs refraction -- what changes
Reflection is a wave bouncing off a barrier: angle of reflection = angle of incidence (measured from the normal); direction changes but speed, wavelength and frequency do not. Refraction is a change of speed entering a new medium, so the wavelength changes in proportion and the direction bends -- but the frequency never changes, it is set by the source.
Lay the calculation out in four steps
Write the equation, convert the units, substitute, then answer with a unit. Setting it out this way secures the method mark even when the arithmetic slips, and the unit -- m/s, Hz or m -- carries a mark of its own on the final line.
Work out the frequency before the speed
When a question supplies a graph or a time rather than a frequency, find first, reading the powers of ten off the axis labels, and check whether the minimum or the maximum frequency is being asked for. Only then substitute into .
For "distinguish", compare the directions
The mark for transverse versus longitudinal is for comparing the direction of oscillation relative to the direction of energy transfer, for both types. Naming examples -- light, sound -- earns nothing on its own, so make the comparison itself explicit in the answer.
Match the command word
State wants one short fact. Describe wants what happens -- in refraction the speed and wavelength change and the direction may bend. Explain wants the reason as well: the frequency is fixed, so a change in speed forces a change in wavelength through .
Cambridge 0654 spec reference: Section P3 "Waves", sub-topic P3.1 (Core + Extended). This leaf covers the Core ideas that waves transfer energy not matter, how wave motion is shown with a rope, spring and ripple tank, the wave features (wavelength, frequency, crest, trough, amplitude, wave speed), the wave equation , and reflection and refraction of waves; plus the Extended ideas that distinguish transverse waves (electromagnetic radiation, water waves, S-waves) from longitudinal waves (sound, P-waves), and describe diffraction through a narrow gap and the effect of wavelength and gap size on it.
Ray-optics detail (the normal, refractive index, critical angle, lenses), the electromagnetic-spectrum order, and the audible range belong to the sibling leaves P3.2, P3.3 and P3.4 and are not covered here.
where = wave speed (m/s), = frequency (Hz) and = wavelength (m).
Rearranged forms: and .
Definitions (mark-scheme form):
(Core) Define the wavelength of a wave and give its symbol and unit.
A wave travels along a stretched rope. It has a frequency of 5 Hz and a wavelength of 0.4 m. Calculate the speed of the wave, showing your working. (2 marks)
