Waves
Waves transfer energy through a medium or field without permanently transporting the medium as a whole.
Complete revision notes
1. Introduction
Mechanical waves travel through a medium; electromagnetic waves do not require one. Medium particles oscillate about equilibrium as the disturbance travels.
2. Transverse and longitudinal waves
Transverse particles oscillate perpendicular to wave travel; longitudinal particles oscillate parallel, creating compressions and rarefactions. Sound in air is longitudinal.
3. Displacement relation in a progressive wave
A progressive sinusoidal wave may be y=A sin(kx−ωt+φ) for travel in +x, with k=2π/λ and ω=2πf.
4. The speed of a travelling wave
Wave speed v=fλ=ω/k. In a given medium, speed is set by the medium and wave type; frequency and wavelength change inversely if speed stays constant.
5. The principle of superposition of waves
Superposition adds displacements algebraically. In-phase waves interfere constructively; opposite-phase waves can partially or fully cancel.
6. Reflection of waves
At a fixed end reflected pulses invert; at a free end they do not. Opposite travelling waves can form standing waves with nodes and antinodes.
7. Beats
Beats occur when two close frequencies superpose; f_beat=|f₁−f₂|, giving periodic loudness variations.
Formula sheet
Use SI units, state assumptions and directions before substitution, show working and round only the final result.
Worked example
Common errors and exam checklist
Distinguish wave speed from particle speed; check phase sign for travel direction; beats need close frequencies.
- Write the relevant law before substituting values.
- Show steps, units and signs/directions.
- Check that the final answer is physically reasonable.
Original StudyNest revision material. Use alongside your textbook, diagrams and teacher's notes.