Answer to Question #281046 in Physics for Ahmad

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

$y(x,t) = 10 \sin⁡(2πx) \cos⁡(15πt)=0\\\cos⁡(15πt)=0\\15πt=\frac{\pi}{2}+\pi n\\t=\frac{1}{30}+\frac{n}{15}$