Energy Transport

Wave transports ENERGY without transporting matter. Particles oscillate locally; energy moves at wave speed.

Power transmitted by a sinusoidal wave on a string: P = ½μω²A²v.

Quadratic in BOTH amplitude (A) and frequency (ω). Doubling either ⇒ quadruple power.

Intensity I = P/area. For 3D sound waves: I = ½ρvω²A² (W/m²).

Inverse-square law: from a point source, I drops as 1/r² (spreading over sphere of area 4πr²).

Sound levels: decibel scale is logarithmic; 10 dB increase = 10× intensity = √10 ≈ 3.16× amplitude.

Damping/absorption: real waves lose energy as they travel — light absorbed by glass, sound absorbed by walls.

Energy in standing waves: bounces back and forth, no net transport.