1506 Wave Interference Boundary Conditions and Superposition

We use interference to refer to what happens when two or more waves pass through the same region at the same time.

The Principle of Superposition

$\begin{aligned} y(x, t) = y_1(x, t) + y_2(x, t) \end{aligned}$

Exercises

32, 33, 34, 35

15.32 Interference of Triangular Pulses. Two triangular wave pulses are traveling toward each other on a stretched string as shown in Fig. E15.32. Each pulse is identical to the other and travels at $2.00 \text{ cm/s}$. The leading edges of the pulses are $1.00 \text{ cm}$ apart at $t = 0$. Sketch the shape of the string at $t = 0.250s, t = 0.500s, t = 0.750s, t = 1.000s$, and $t = 1.250 s$.

15.33 Suppose that the left-traveling pulse in Exercise 15.32 is below the level of the unstretched string instead of above it. Make the same sketches that you did in that exercise.

15.34 Two pulses are moving in opposite directions at $1.0\text{ cm/s}$ on a taut string, as shown in Fig. E15.34. Each square is $1.0$ cm. Sketch the shape of the string at the end of (a) $6.0 s$; (b) $7.0 s$; (c) $8.0 s$.

15.35 Interference of Rectangular Pulses. Figure E15.35 shows two rectangular wave pulses on a stretched string traveling toward each other. Each pulse is traveling with a speed of $1.00 \text{ mm/s}$ and has the height and width shown in the figure. If the leading edges of the pulses are $8.00$ mm apart at $t = 0$, sketch the shape of the string at $t = 4.00 s, t = 6.00 s$, and $t = 10.0 s$.