= Amplitude scaling along a slowly tapered string
{title2=$A\propto Z^{-1/2}\propto\rho^{-1/4}$}
A static lossless taper preserves <frequency>. If <characteristic impedance> varies slowly on the local <wavelength> scale, reflection is small and mean <power> $Z\omega^2A^2/2$ is conserved. At fixed <tension> this gives the displayed amplitude law, while <wave speed> and <wavelength> scale as $\rho^{-1/2}$. A long section containing an abrupt step is not automatically adiabatic.
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