Chapter 17, Problem 72PQ

A The equation of a harmonic wave propagating along a stretched string is given as

$y(x,t)=y_{\max }\sin \left[2\pi \left(\frac{x}{a}-ft\right)\right]$

where a is a constant and f is the frequency. If the magnitude of the maximum vertical speed

$v_{y,\max }={\frac{\partial y}{\partial t}|}_{\max }$

is equal to three times the propagation speed, what is the value of a? Express your answer in terms of y_max.