Waves
This section covers Waves. The exam tests wave properties, reflection, refraction, diffraction, superposition, standing waves, resonance and the Doppler effect.
Core rules
- Waves transfer energy without transferring matter. Transverse oscillations are perpendicular to propagation; longitudinal oscillations are parallel.
- Wave speed v = fλ. Frequency is set by the source and does not change when a wave enters a new medium; speed and wavelength change.
- Superposition adds displacements. Constructive interference occurs when waves arrive in phase; destructive interference occurs when they arrive in antiphase.
- Standing waves form when two waves of equal frequency and amplitude travel in opposite directions. Nodes have zero amplitude; antinodes have maximum amplitude.
- For a source moving towards an observer, the observed frequency is higher; for a source moving away, it is lower.
Worked example
A wave has frequency 50 Hz and wavelength 0.80 m. Its speed is v = fλ = 50 × 0.80 = 40 m s⁻¹. Its period is T = 1/f = 1/50 = 0.020 s. If this wave passes into a medium where its speed doubles to 80 m s⁻¹, its frequency remains 50 Hz, so the new wavelength is λ = v/f = 80/50 = 1.6 m.
Traps
Do not change frequency across a boundary; change speed and wavelength instead. Do not confuse amplitude with intensity: intensity is proportional to amplitude squared. Nodes are points of zero displacement, not points of zero wave speed. In the Doppler effect, the observed frequency changes, not the source frequency. For standing waves, adjacent nodes are separated by half a wavelength.