Chapter 16, Problem 76P

A standing wave results from the sum of two transverse traveling waves given by

$\begin{array}{l}{y}_1=0.050\text{ cos}\left(\pi x-4\pi t\right)\hfill \\ \text{and}{y}_2=0.050\text{ cos}\left(\pi x+4\pi t\right),\hfill \end{array}$

where x, y₁ and y₂ are in meters and t is in seconds. (a) What is the smallest positive value of x that corresponds to a node? Beginning at t = 0, what is the value of the (b) first, (c) second, and (d) third time the particle at x = 0 has zero velocity?