 Solution

Let the common tension be T, the linear mass densities be ${\mu }_1<{\mu }_2$ and the speeds be $c_j=\sqrt{T/{\mu }_j}$, so $c_2<c_1$. Displacement and transverse-force continuity give the displacement coefficients at a string junctionThe reflected triangular pulse is inverted, has smaller height $|r|H$, unchanged spatial width and unchanged speed, and travels left. Its left-to-right asymmetric profile is reversed as well as vertically inverted. The transmitted pulse remains upright, has smaller height tH, travels more slowly, and has width $W{c}_2/c_1$. The string-pulse width mapping at a junction leaves its temporal duration unchanged. The transmitted slopes are steeper by $2c_1/(c_1+c_2)$; the reflected slope magnitudes are smaller by $|r|$.

The density ratio is unspecified, so only these inequalities are determined. The original plot below illustrates ${\mu }_2/{\mu }_1=4$, giving $r=-1/3$, $t=2/3$ and half-width transmission; it is not a numerical reading of the examination figure.