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Having established what a wave is (Lesson 1), we now need the quantitative vocabulary to describe one. This lesson introduces the six core parameters of any progressive wave — displacement, amplitude, wavelength, frequency, period and phase difference — together with the two essential relationships between them:
v = fλ (the wave equation) T = 1/f (period and frequency are reciprocals)
These relationships will be used in every remaining lesson of the module. Mastery of them is non-negotiable for A-Level physics.
Displacement (x or y) is the distance of a particle of the medium from its equilibrium position at a given instant, measured in the appropriate direction (perpendicular to the direction of travel for a transverse wave, parallel for a longitudinal wave).
Displacement is a signed quantity: it can be positive or negative depending on which side of the equilibrium position the particle is. Over one complete oscillation, a particle's displacement passes through zero twice (as it crosses equilibrium) and reaches its maximum value twice (once positive, once negative).
Unit: metre (m), though for small oscillations you will often see it quoted in millimetres or micrometres.
The amplitude (A) of a wave is the maximum displacement of a particle from its equilibrium position. It is the peak value of the signed displacement — a strictly positive number.
For a sinusoidal wave, every particle has the same amplitude (ignoring damping). The amplitude is a property of the wave, set by how much energy it carries, and does not change as the wave propagates through a non-absorbing medium.
Key fact: the energy (and therefore power) carried by a wave is proportional to A². Doubling the amplitude quadruples the energy carried per unit time.
Exam Tip: Be careful with units. If a transverse water wave has amplitude 5 cm, this is the distance from the mean level to the crest, not the crest-to-trough distance (which would be 2A = 10 cm).
The wavelength (λ) of a wave is the distance between two successive points in phase — typically taken as the distance between two neighbouring crests, or two neighbouring troughs, or two neighbouring compressions.
Unit: metre (m). For visible light, wavelength is in the range ~400–700 nm (nanometres); for radio waves it can be metres or kilometres; for X-rays it is around 10⁻¹⁰ m.
If you plot displacement against position at a fixed instant of time, the wavelength is the horizontal distance between two successive peaks of the graph.
The frequency (f) of a wave is the number of complete oscillations (or complete waves) passing a point per unit time.
Unit: hertz (Hz), where 1 Hz = 1 oscillation per second = 1 s⁻¹.
Frequency is set by the source of the wave and does not change when the wave passes into a different medium. (This is important when we study refraction in Lesson 5: when light enters glass, its speed and wavelength both decrease, but its frequency stays the same. Colour is determined by frequency, which is why colour does not change on refraction.)
Typical frequencies you will meet at A-Level:
| Phenomenon | Typical frequency |
|---|---|
| Deep infrasound | < 20 Hz |
| Audible sound | 20 Hz – 20 kHz |
| Ultrasound | > 20 kHz |
| Mains AC (UK) | 50 Hz |
| FM radio | ~100 MHz |
| Microwave ovens | 2.45 GHz |
| Visible light | ~430–750 THz |
| X-rays | ~10¹⁸ Hz |
The period (T) of a wave is the time for one complete oscillation (the time taken for one full wave to pass a fixed point).
Unit: second (s).
Period and frequency are reciprocals of one another:
T = 1/f and equivalently f = 1/T
This is the simplest and most often-used wave relationship. If a speaker emits a pure 440 Hz tone (middle A on a piano), the period of the sound wave is T = 1/440 Hz = 2.27 × 10⁻³ s = 2.27 ms.
The single most important equation in wave physics is:
v = fλ
where:
In one complete oscillation (one period T), the wave advances by exactly one wavelength λ. Hence:
v = distance / time = λ / T
Combining with f = 1/T gives v = fλ.
This derivation is worth committing to memory — OCR sometimes asks you to derive the wave equation from first principles in a short-answer question.
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