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AS & A-Level Physics 07 — Waves and Their Properties

AS & A-Level Physics 07 — Waves and Their Properties

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 7 of 26: Waves and their properties. Concepts, worked applications and misconception checks.

Physics EN AS & A-Level
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Describing Waves: Key Terminology

To analyse waves, we use a set of specific terms. The displacement (yy) of a particle is its distance from its equilibrium (rest) position at any instant. The maximum displacement is the amplitude (AA). The wavelength (λ\lambda) is the shortest distance between two points on the wave that are in phase, for example, from one crest to the next. The period (TT) is the time taken for one complete oscillation of a particle. The frequency (ff) is the number of complete oscillations per second, related to the period by f=1/Tf = 1/T. The wave speed (vv) is the speed at which the wave profile propagates. Phase difference describes the relationship between the oscillations of two points. If they reach their maximum displacement at the same time, they are in phase (phase difference of 0∘0^{\circ}). If one reaches a crest while the other is at a trough, they are in antiphase (phase difference of 180∘180^{\circ}).

Key points

  • Displacement (yy): Instantaneous distance from equilibrium.
  • Amplitude (AA): Maximum displacement.
  • Wavelength (λ\lambda): Spatial period of the wave (e.g., crest-to-crest distance).
  • Period (TT): Time for one full oscillation. Frequency (ff) is 1/T1/T.
  • Phase difference: The fraction of a cycle (in degrees or radians) by which one oscillation leads or lags another.

Worked example

Question

A water wave has an amplitude of 0.50 m and a period of 4.0 s. Two points, P and Q, on the water surface are separated by a distance of 3.0 m along the direction of wave travel. The wave speed is 2.0 m/s. What is the phase difference between points P and Q in degrees?

Solution

1. First, find the wavelength (λ\lambda) using the wave equation v=fλv = f\lambda. We need the frequency, f=1/T=1/4.0 s=0.25 Hzf = 1/T = 1/4.0 \text{ s} = 0.25 \text{ Hz}.
2. Rearrange for wavelength: λ=v/f=2.0 m/s/0.25 Hz=8.0 m\lambda = v/f = 2.0 \text{ m/s} / 0.25 \text{ Hz} = 8.0 \text{ m}.
3. The separation x=3.0 mx = 3.0 \text{ m} is a fraction of the wavelength: x/λ=3.0/8.0=0.375x/\lambda = 3.0 / 8.0 = 0.375.
4. One full wavelength corresponds to a phase difference of 360∘360^{\circ}. So, the phase difference ϕ\phi is 0.375×360∘=135∘0.375 \times 360^{\circ} = 135^{\circ}.

The phase difference between points P and Q is 135∘135^{\circ}.

Common pitfalls

  • Confusing period (time per cycle) with frequency (cycles per time). Remember they are reciprocals.
  • Mistaking wavelength for amplitude on a displacement-distance graph. Wavelength is a horizontal distance, while amplitude is a vertical distance.

Prerequisites

  • Requires a qualitative understanding of wave motion before quantifying it.
  • These terms are often represented graphically.
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