Question

A string is rigidly tied at two ends and its equation of vibration is given by
$y=\cos 2\pi t\sin 2\pi x$ then minimum length of string is

• A. $1m$
• B. $\frac{1}{2}m$
• C. $5m$
• D. $2\pi m$

Answer 1

The correct option is B $\frac{1}{2}m$

$y=sin2\pi xcos2\pi t$
$k=2\pi$
We know that
$k=\frac{2\pi }{\lambda }$
So, $\lambda =\frac{2\pi }{k}=\frac{2\pi }{2\pi }=1m.$
Minimum length is $\frac{\lambda }{2}$
So, minimum length required $=\frac{1}{2}m.$