Waves, Sound, and Optics
Core concepts
Know the wave equation v = fλ, the distinction between transverse and longitudinal waves, superposition, and the behaviours of reflection, refraction, diffraction and interference. For sound, understand frequency determines pitch, amplitude determines loudness, and that sound needs a medium. For light, apply Snell's law (n₁sinθ₁ = n₂sinθ₂), total internal reflection when moving to a less dense medium beyond the critical angle, and the lens/mirror equation 1/f = 1/u + 1/v with magnification m = v/u.
Common traps
- Frequency is fixed when a wave crosses a boundary; speed and wavelength change.
- Diffraction is greatest when the gap is comparable to the wavelength - a common conceptual question.
- Real vs virtual images: a converging lens gives a virtual, upright, magnified image when the object is inside the focal length.
- Sound speed is higher in solids than gases; frequency does not change with medium.
- Confusing interference (superposition of coherent waves) with resonance (driven near natural frequency).
Worked example
Light passes from water (n = 1.33) to air. Critical angle: sinθc = 1/1.33 ≈ 0.752, so θc ≈ 48.8°. Any ray striking the boundary at more than this angle is totally internally reflected - the basis of optical fibres.
Rule of thumb
For any wave problem, write v = fλ first and decide which quantities are conserved across a boundary.