Energy Transport
P = ½μvω²A² — power along a string.
Key Notes
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.
Formulas
Power on string (sinusoidal)
Quadratic in A and ω.
Sound intensity (3D)
Power per unit area.
Inverse-square law
Isotropic point source.
Decibel scale
Logarithmic measure of intensity.
Important Points
Energy transport is the PURPOSE of waves — they move energy efficiently across distance.
Power ∝ A² and ω² — doubling either quadruples energy flow.
Inverse-square law for point sources: doubling distance quarters intensity.
Plane waves: intensity is constant with distance (in non-absorbing medium).
Whisper at 30 dB ≈ 10⁻⁹ W/m². Conversation 60 dB. Concert 120 dB.
Standing wave: ZERO NET energy transport — energy oscillates between halves.
Energy Transport notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.