= Envelope
{disambiguate=waves}
{wiki}
= Wave envelope
{synonym}
A <wave envelope> is a slowly varying <wave amplitude> multiplying a rapidly oscillating <carrier wave>. For a complex wavefield $\psi=A(x,t)e^{i(k_0x-\omega_ct)}$, its nonnegative amplitude envelope is $|A|=|\psi|$; the complex $A$ can also encode a slowly varying <wave phase>. This choice distinguishes the amplitude envelope from a signed modulation factor, such as the cosine factor in a two-tone <superposition>. A slowly varying <wave envelope> is useful when the carrier's <wavelength> and <period> are short compared with its variation scales. Strong overlap between distinct packets or a broad <frequency spectrum> can spoil a unique carrier-envelope interpretation.
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