Answer to Question #195521 in Mechanics | Relativity for Mohammad Balhas

Question

A standing wave has the following wave-function: y(x,t) = 0.2 sin(πx) cos⁡(12πt), where x and y are in meters, and t is in seconds. If the length of the string is L = 2 m and it is fixed at both ends, then the harmonic, n, in which the string is vibrating is:

n = 3

n = 5

n = 4

n = 6

n = 2

Answer 1

$\frac{2\pi}{\lambda}=\pi\implies \lambda =2~m,$

$12\pi=2\pi\nu\implies \nu=6~Hz,$

$v=\lambda \nu=2\cdot 6=12~\frac ms,$

$\nu=\frac{nv}{2L}\iff 6=\frac{12n}{2\cdot 2}\implies \\n=2.$