Halliday, Resnick & Walker — Waves-I: Problem 40

40 A standing wave pattern on a string is described by \( y(x, t) = 0.040 (\sin 4\pi x)(\cos 40\pi t) \), where \( x \) and \( y \) are in meters and \( t \) is in seconds. For \( x \ge 0 \), what is the location of the node with the (a) smallest, (b) second smallest, and (c) third smallest value of \( x \)? (d) What is the period of the oscillatory motion of any (nonnode) point? What are the (e) speed and (f) amplitude of the two traveling waves that interfere to produce this wave? For \( t \ge 0 \), what are the (g) first, (h) second, and (i) third time that all points on the string have zero transverse velocity?