Rule 28 of 36 · Chapter IV — Fields & Waves
The medium shapes the message
Why this rule exists
A wave's speed, wavelength, and even its shape are properties of the medium it travels through, not of the source. The medium's stiffness and inertia set the propagation speed; when that speed depends on frequency, different components travel at different rates and the signal spreads. The message is carried, but the medium rewrites how it arrives.
In practice
Before predicting how a wave arrives, characterize the medium: its wave speed, and whether that speed varies with frequency (dispersion) or direction (anisotropy). For a pulse in a dispersive medium, distinguish phase velocity from group velocity — the latter carries the energy and information. Expect attenuation, refraction at boundaries, and reshaping of the waveform over distance.
When it doesn't apply
In a non-dispersive, lossless, linear medium the waveform is preserved and this reshaping vanishes. At high amplitudes the medium responds nonlinearly, so the wave alters the medium in turn and superposition fails.