Energy lost between two amplitudes
Read the amplitude at two positions/times off the decaying envelope → energy lost to resistive forces = ½mω²(y₀₁² − y₀₂²) — the Oscillations formula carried over. Intensity ratio between the same two points: I₂/I₁ = (y₀₂/y₀₁)².
What this actually means
A decaying envelope on a y–t graph means damping: energy leaving to resistive forces. Read the amplitude at two moments and the loss is ½mω²(y₀₁² − y₀₂²), straight from Topic 8.
Distinguish this from an amplitude fall along a y–x graph caused by spreading. In spreading, energy is NOT lost, it is diluted over a growing wavefront; writing 'energy lost' there kills the explanation mark.
Between the same two points, the intensity ratio is the amplitude ratio squared, as always.
Writing 'energy lost' for spreading — spreading dilutes energy over area; only damping removes it.
Prove it — watch it be true
- Open the spreading-vs-damping twin graphs
- Damping side: read two envelope amplitudes and watch the ΔE readout
- Spreading side: amplitude falls too, but ΔE stays zero — nothing was lost