= 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 junction>
$$
\boxed{r=\frac{c_2-c_1}{c_2+c_1}<0,\qquad t=\frac{2c_2}{c_1+c_2},\quad0<t<1.}
$$
The 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 $Wc_2/c_1$. 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.
\Image[/past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2010/paper-1-pa2010-pulse-junction.png]
{title=Pulse junction}
{description=Illustrative density ratio four; reflection inverts the pulse and transmission compresses its width.}
{source=paper-1-pa2010-pulse-junction.py}
Back to article page
