= Free-end reflection of a transverse string wave
{title2=$\partial_x\psi=0,\quad r_\psi=+1$}
At a free termination of a taut string, zero transverse <force> imposes a <Neumann boundary condition>. Incident and reflected displacement amplitudes add with equal sign so their slopes cancel. The endpoint is a displacement antinode, all incident <power> is reflected, and the flux $-T\psi_x\psi_t$ through the boundary vanishes. This is a transverse-wave <boundary condition>, distinct from the quantum open-string usage of similar notation.
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