Waves

What waves covers

Oscillations that travel, and the patterns they produce when they meet each other, a boundary or a gap. Superposition is the idea the unit is built around, and it returns later in electron diffraction and in astronomy. Two AQA required practicals sit here, on stationary waves and on interference, so the measurement technique is examinable too.

The main ideas

• Amplitude, wavelength, frequency, period and phase difference, and the difference between a displacement-distance and a displacement-time graph.
• Transverse against longitudinal, and polarisation as evidence that light is transverse while sound in air is not.
• Stationary waves: nodes, antinodes, their spacings, and the harmonics of a string and of open and closed air columns.
• Refraction, Snell's law, the critical angle and total internal reflection, with optical fibres as the application.
• Diffraction at a single slit, and what slit width and wavelength do to the pattern.
• Two-source interference: path difference, coherence and fringe spacing, then the grating with its orders.
• Lenses, ray diagrams and the thin lens equation.

The equations it turns on

c = fλ     f = 1T$c = f\lambda \qquad f = \frac{1}{T}$c = fλ f = 1/T

the wave equation, and period from frequency

n₁sin θ₁ = n₂sin θ₂      sin θ_c = n₂n₁$n_1\sin\theta_1 = n_2\sin\theta_2 \qquad \sin\theta_c = \frac{n_2}{n_1}$n_1 sin θ_1 = n_2 sin θ_2 sin θ_c = n_2/n_1

refraction, and the critical angle

w = λDs$w = \frac{\lambda D}{s}$w = λD/s

fringe spacing in Young's double-slit experiment

dsin θ = nλ$d\sin\theta = n\lambda$d sin θ = nλ

the grating, with d from the lines per millimetre

λ_n = 2Ln for a string     λ₁ = 4L for a closed pipe$\lambda_n = \frac{2L}{n} \text{ for a string} \qquad \lambda_1 = 4L \text{ for a closed pipe}$λ_n = (2L/n) for a string λ_1 = 4L for a closed pipe

allowed stationary-wave wavelengths

1u + 1v = 1f     P = 1f$\frac{1}{u} + \frac{1}{v} = \frac{1}{f} \qquad P = \frac{1}{f}$1/u + 1/v = (1/f) P = 1/f

the thin lens equation, and power in dioptres

Where it usually goes wrong

• A stationary wave is not a wave that has stopped. It is two waves travelling in opposite directions, it transfers no energy along the medium, and every point within one loop oscillates in phase.
• Waves diffract at any gap. The spreading is greatest when the gap is comparable with the wavelength, not only when it is smaller.
• In the critical angle formula the smaller refractive index goes on top, and the light has to start in the denser medium.
• The three lengths in w = lambda D / s arrive in nanometres, millimetres and metres, and converting all three first prevents most lost marks here.

Where to start

Progressive waves first for the vocabulary, then longitudinal and transverse, then stationary waves. Take diffraction, the double slit and gratings in that order, since each uses the one before. Lenses is self-contained and can be taken at any point.