Oscillations and Waves
What this domain tests
Oscillations and Waves tests simple harmonic motion, pendulum and spring oscillations, the wave equation, superposition, standing waves, beats and the Doppler effect.
Core rules
- SHM: a = −ω²x; x = A sin(ωt + φ); v = ω√(A² − x²); T = 2π/ω.
- Simple pendulum: T = 2π√(L/g) for small angles. Spring: T = 2π√(m/k).
- Wave: y = A sin(ωt − kx); speed v = ω/k = fλ.
- Beats frequency = |f₁ − f₂|.
- Doppler: f' = f(v ± v_o)/(v ∓ v_s), with signs depending on approach or recession.
Worked example
A wave is y = 0.02 sin(100t − 2x) in SI units. Compare with y = A sin(ωt − kx): ω = 100 rad/s, k = 2 rad/m. Speed v = ω/k = 50 m/s, frequency f = ω/2π ≈ 15.9 Hz and wavelength λ = 2π/k ≈ 3.14 m. The argument of sine must be in radians; mixing degrees and radians is a frequent calculator error.
Traps
Using the pendulum formula for large amplitudes; forgetting that T is independent of amplitude only for small oscillations; adding frequencies instead of subtracting for beats; getting Doppler signs wrong when source and observer move in the same direction; confusing wave speed with particle speed.