= Displacement coefficients at a string junction
{title2=$r=(c_2-c_1)/(c_2+c_1),\quad t=2c_2/(c_1+c_2)$}
For transverse waves on two strings at common <tension>, displacement continuity gives $1+r=t$, while transverse-force continuity gives $(1-r)/c_1=t/c_2$. Solving gives the displayed displacement-amplitude coefficients. A denser transmitted string has lower speed and a negative reflected coefficient. The energy fractions are $r^2$ and $(c_1/c_2)t^2$, summing to1. These are displacement coefficients; force or power-normalized wave amplitudes use different conventions.
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