Question

A standing wave, generated on a string of length L, is represented by the following mathematical expression y(x,t) = 10 sin⁡(2πx) cos⁡(15πt). At what times would all the elements of the string have zero displacement [y(x,?) = 0]?

Answer 1

$y(x,t) = 10\sin⁡ (2πx) \cos⁡(15πt),$

$y(x,t)=0,$

$\cos⁡(15πt)=0,$

$15\pi t=\frac{\pi}2+\pi n,~n\in \Z,$

$t=\frac1{30}+\frac n{15},~n\isin\Z.$