Halliday, Resnick & Walker — Waves–I: Problem Problem_76

A standing wave results from the sum of two transverse traveling waves given by \[y_1 = 0.050 \cos(\pi x - 4\pi t)\] and \[y_2 = 0.050 \cos(\pi x + 4\pi t),\] where \(x, y_1\), and \(y_2\) 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?