Skip to contentQuick reference: waves & sound
Core relations
- wave speed: \(v = f\lambda\)
- period–frequency: \(T = 1/f\)
- wavelength: \(\lambda = v/f\)
Doppler (source → observer)
- approach: \(f’=\dfrac{v}{v-v_s}f\) (pitch ↑, \(\lambda\) ↓)
- recede: \(f’=\dfrac{v}{v+v_s}f\) (pitch ↓, \(\lambda\) ↑)
Standing waves
- node: phase diff \(180^\circ\) (destructive)
- antinode: \(0^\circ\) or \(360^\circ\) (constructive)
Amplitude & energy
- \(E \propto A^2\) (mechanical waves)
- energy loss → amplitude decreases
Wave types
- longitudinal: motion ∥ travel (sound in air)
- transverse: motion ⟂ travel (string ripple, light)
EM spectrum cue
- ultraviolet has shorter wavelength than visible: \(\lambda_{\text{UV}} < \lambda_{\text{visible}}\)
- higher \(f\) → shorter \(\lambda\) (since \(v=c\))
