= Periodic reflection for a fixed-end string
{title2=$y=f(ct-x)-f(ct+x),\quad f(s+2L)=f(s)$}
Zero values at both endpoints of a length-$L$ string allow the <D'Alembert formula> to be written with opposite travelling waves and a $2L$-periodic profile. This represents reflection with sign reversal at each fixed endpoint. For positive-time boundary conditions, periodicity concerns the arguments visited by the string solution; unused profile values can be defined by periodic extension.
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