Mechanical and electromagnetic waves; sound and light
Wave questions in the PAU cover the wave equation, energy and intensity, standing waves in strings and pipes, and the geometric and wave optics of light: Snell's law, lenses and mirrors, interference and diffraction. Expect one numeric optics problem and one qualitative question about wave properties, often including polarisation.
Core rules
- v = λf; for a string v = √(T/µ); for sound in air v ≈ 340 m/s at room temperature.
- Intensity I = P/S and I ∝ A²; a point source in three dimensions gives I ∝ 1/r². Sound level β = 10 log(I/I₀) dB with I₀ = 10⁻¹² W m⁻².
- Standing waves: string fixed at both ends and pipe open at both ends give λₙ = 2L/n; a pipe closed at one end gives only odd harmonics, λₙ = 4L/n with n odd.
- Doppler: f′ = f(v ± v₀)/(v ∓ v_s), signs chosen so that approach raises the frequency.
- Snell: n₁ sinθ₁ = n₂ sinθ₂; n = c/v; total internal reflection when sinθ_c = n₂/n₁.
- Double slit: bright fringes at d sinθ = mλ, spacing Δy = λL/d. A grating obeys the same condition but gives sharper maxima. Polarisation proves light is transverse; sound cannot be polarised.
Worked example
Light of 633 nm falls on two slits 0.10 mm apart, with the screen 2.0 m away. The fringe spacing is Δy = λL/d = (633×10⁻⁹ × 2.0)/(1.0×10⁻⁴) = 1.27×10⁻² m, about 1.3 cm between consecutive bright fringes. Halving the slit separation would double the spacing, which is why the pattern width measures d directly. The angle is small (about 0.36°), so the small-angle approximation used here is safe.
Marks lost here
Writing I ∝ A instead of A². Using the open-pipe harmonic set for a closed pipe. Mixing the Doppler sign convention and predicting a lower frequency for an approaching source. Applying Δy = λL/d to a grating without checking the small-angle condition. Forgetting that light bends towards the normal when it enters a medium of higher refractive index.