Answer to Question #195532 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

Clear selection

Answer 1

Length of string, $L=2\space m$

Comparing the given equation with standard equation

$y=A\sin (kx)\cos(\omega t)$

$k=\pi$

$k=\dfrac{2\pi}{\lambda}$

$\lambda=\dfrac{2\pi}{\pi}$

$\lambda=2\space m$

$n=\dfrac{2L}{\lambda}=\dfrac{2\times2}{2}$

$n=2$