2) [15pts] King Worked Example (Ch. 5): A wave on a string crosses two boundaries, one at $x = 0$ and one at $x = L$, as shown in the figure below. Assume that the impedance in each region is $Z_1 < Z_2 < Z_3$.
$R_{12}, T_{12}, T_{21}$ $R_{23}, T_{23}$
y1
y2
y3
y4
y6 y5
string 1 string 2 string 3
x = 0 x = L
c. Consider the simpler case where $Z \sim 1/v$ and $v = \frac{\omega}{k}$. For what length, $L$, will reflection waves $y_4$ and $y_6$ perfectly cancel (destructively superimpose)?