Waves
Waves tests wave motion, the wave equation, superposition, standing waves, resonance, diffraction, interference, polarisation and the Doppler effect. The exam expects you to connect a physical situation to a wave property and to calculate frequency, wavelength, speed or path difference.
Core rules
- The wave equation is v = fλ, and period T = 1/f. Frequency is set by the source and does not change when a wave enters a new medium; speed and wavelength do.
- Transverse waves vibrate perpendicular to energy transfer; longitudinal waves vibrate parallel to it. Polarisation is evidence that light is transverse.
- Superposition adds displacements. Coherent sources with path difference nλ give constructive interference; path difference (n + ½)λ gives destructive interference.
- A string fixed at both ends has standing-wave wavelengths λ = 2L/n, so the fundamental is λ = 2L.
- Diffraction is greatest when the gap is about one wavelength or smaller.
- The Doppler effect changes observed frequency when source and observer have relative motion.
Worked example
A string of length 1.60 m is fixed at both ends and vibrates in its fundamental mode at 40.0 Hz. Find the wavelength and speed. For the fundamental, L = λ/2, so λ = 2L = 3.20 m. Then v = fλ = 40.0 × 3.20 = 128 m/s. The next harmonic has twice the frequency, 80.0 Hz, and wavelength 1.60 m, because the string now has two half-wavelengths.
Traps
Convert centimetres to metres before using v = fλ. Do not assume frequency changes on refraction. Do not confuse nodes with antinodes: nodes have zero displacement. Check whether a path difference condition is for constructive or destructive interference. A standing wave does not transfer net energy along the string.