= Displacement cancellation without slope cancellation in crossing pulses
For <two-sided string data with zero slope>, take $f(t)=\sin(\pi t/a)$ on $[-a,a]$ and zero outside. At $x=ca/2$, the <displacement> vanishes throughout $|t|<a/2$, whereas the spatial <derivative> is $y_x=-\pi\sin(\pi t/a)/(ca)$. Cancellation along a line in spacetime need not cancel the <derivative> transverse to that line. At $x=ca,t=0$, however, oddness gives $y(x,0)=0$ for every $x$, so the <spatial derivative> is zero even though its one-sided temporal limits there differ.
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