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Waves
Eduqas A Level Physics — Revision Notes
Component 3: Light, Nuclei and Options · Waves topics
Types of Waves
A wave transfers energy without transferring matter. There are two fundamental types based on the direction of oscillation relative to the direction of energy transfer.
Transverse and Longitudinal Waves
Transverse waves: oscillations are perpendicular to the direction of energy propagation. Examples: all electromagnetic waves, waves on strings, water surface waves. Longitudinal waves: oscillations are parallel (along the same direction) to the direction of energy propagation. Examples: sound waves, ultrasound, seismic P-waves. Only transverse waves can be polarised.
Wave Properties
Key Wave Quantities
Wavelength (λ): Distance between two successive points in phase (e.g. crest to crest). Units: m. Frequency (f ): Number of complete oscillations per second. Units: Hz. Period (T ): Time for one complete oscillation. T = 1/f. Amplitude (A): Maximum displacement from equilibrium. Intensity ∝ A^2. Wave speed (v): v = f λ Phase difference: Measured in radians or degrees. Points λ apart are in phase; points λ/2 apart are antiphase.
Superposition and Interference
When two waves meet, their displacements add together at every point. This is the principle of superposition.
Interference Conditions For two coherent sources (same frequency, constant phase relationship): Constructive interference (reinforcement): path difference = nλ (n = 0, 1 , 2 ,.. .). Phase difference = 0, 2 π, 4 π,... giving a bright fringe or loud sound. Destructive interference (cancellation): path difference = (n + 12 )λ. Phase difference = π, 3 π,... giving a dark fringe or silence.
Double Slit (Young’s Experiment) Monochromatic light through two slits separated by d produces interference fringes on a screen at distance D. The fringe separation is:
w =
λD d This experiment proves light is a wave. To get bright fringes you need coherent, monochromatic sources — hence the two slits from one laser or one slit from a monochromatic lamp.
Diffraction Grating A diffraction grating with N lines per mm has a slit spacing d = 1/N (in mm). The condition for bright maxima is: d sin θ = nλ, n = 0, ± 1 , ± 2 ,... n is the order. The grating produces much sharper, more widely spaced maxima than two slits — useful for measuring wavelengths precisely.
Stationary (Standing) Waves
When two waves of equal frequency and amplitude travel in opposite directions, their super- position creates a stationary wave. The pattern does not move along; instead, some points (nodes) never move, and others (antinodes) oscillate with maximum amplitude.
Nodes and Antinodes Node: A point of zero displacement at all times. Occurs where the two waves always cancel. Antinode: A point of maximum displacement. Occurs where the two waves always reinforce. Adjacent nodes are separated by λ/2.
Harmonics in Strings and Pipes For a string of length L fixed at both ends (nodes at both ends):
L =
nλ 2
=⇒ λn =
2 L
n
, fn =
nv 2 L The fundamental (n = 1) has frequency f 1 = v/ 2 L. Higher harmonics are integer multiples. For open pipes (antinodes at both ends): same formula. For closed pipes (node at closed end, antinode at open end): only odd harmonics occur, fn = (2n − 1)v/ 4 L.
Refraction and Snell’s Law
When waves pass from one medium to another, speed and wavelength change, but frequency stays constant. This change in speed causes a change in direction called refraction.
n 1 sin θ 1 = n 2 sin θ 2 (Snell’s Law)
Exam Tips
The wave equation v = f λ applies to all waves. Don’t mix up v (wave speed) and vs (source speed) in Doppler. For TIR: the angle must be measured from the normal, not the surface. Stationary waves store energy; progressive waves transfer it. In refraction: frequency is constant; wavelength and speed both change.
