Question

The equation of a stationary wave in a medium is given as $y=\sin \omega t\cos kx$. The length of a loop in fundamental mode is

• A. $\frac{\pi }{2K}$
• B. $\frac{\pi }{K}$
• C. $\frac{2\pi }{K}$
• D. $\frac{K}{\pi }$

Answer 1

Answer: (B)

$\frac{\pi }{K}$

$Y=0\Rightarrow \cos kx=0$
$kx=\left(\frac{n+1}{2}\right)\pi$
for fundamental mode. $n=0$
$\Rightarrow x=\frac{\pi }{2k}=\frac{\lambda }{4}$
$\therefore$ length in fundamental
$\frac{\lambda }{2}=2\left(\frac{\pi }{2k}\right)$
$=\frac{\pi }{k}$