= Annual ground-temperature wave
{title2=$T-T_0=-T_Ae^{-z/\delta}\cos(\omega t-z/\delta)$}
A sinusoidal surface <temperature> applied to a homogeneous semi-infinite conductor produces a periodic depth profile with penetration length $\delta=\sqrt{2\kappa/(\omega C)}$. It follows by substituting a complex exponential into $C\partial_tT=\kappa\partial_z^2T$ and taking the root that decays at depth. A depth $z$ attenuates the amplitude by $e^{-z/\delta}$ and delays the phase by $z/\delta$. This is <diffusion> with phase delay, rather than a nondispersive travelling wave.
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