Chapter 1, Problem 8P

Two waves on a string are given by the following functions:

  $\begin{array}{l}{y}_1\left(x,t\right)=4\cos \left(20t-30x\right)\left(\text{cm}\right)\\ y_1\left(x,t\right)=-4\cos \left(20t+30x\right)\left(\text{cm}\right)\end{array}$

 where x is in centimeters. The waves are said to interfere constructively when their superposition $\left|y_{\text{s}}\right|=\left|y_1+y_2\right|$ is a maximum, and they interfere destructively when $\left|y_{\text{s}}\right|$ is a minimum.

1. (a) What are the directions of propagation of waves y₁(x, t) and y₂(x, t)?
2. (b) At $t=\left(\pi /50\right)$ s, at what location x do the two waves interfere constructively, and what is the corresponding value of $\left|y_{\text{s}}\right|$?
3. (c) At $t=\left(\pi /50\right)$ s, at what location x do the two waves interfere destructively, and what is the corresponding value of $\left|y_{\text{s}}\right|$?