Waves & harmonics
Start with the model and its assumptions. These relationships use SI units unless you convert every quantity consistently.
Waves & harmonics
| Relationship | Formula | When it applies |
|---|---|---|
| Wave relationships | v = fλ = ω/k; ω = 2πf; k = 2π/λ | Phase speed for a monochromatic wave. |
| Sound level | β = 10 log₁₀(I/I₀); I₀ = 10⁻¹² W/m² | Add incoherent sound intensities before converting to decibels. |
| Refraction & photons | n₁ sin θ₁ = n₂ sin θ₂; E = hf = hc/λ; p = h/λ | Angles are measured from the normal. Photon equations use vacuum wavelength; energy is per photon. |
| Mass–spring motion | ω₀ = √(k/m); T = 2π√(m/k) | Ideal linear spring, no damping. |
| Pendulums | Tsimple ≈ 2π√(ℓ/g); Tphysical ≈ 2π√(I/(mgd)) | Small angular amplitude; d is pivot-to-centre-of-mass distance. |
| Standing waves | λₙ = 2ℓ/n; fₙ = nv/(2ℓ) | String fixed at both ends; n loops and n + 1 nodes including endpoints. |
| Damping | x = A e⁻ᵞᵗ cos(ωdt + φ); ωd² = k/m − γ² | Underdamped viscous damping; γ = b/(2m). Exponential decay does not stop at a finite time. |
Find definitions and the original reference tables in the glossary →