In the equation for a stationary wave given by $y = 5 \cos \frac{\pi x}{25} \sin 100\pi t$ ($x$ is in cm and…
In the equation for a stationary wave given by $y = 5 \cos \frac{\pi x}{25} \sin 100\pi t$ ($x$ is in cm and $t$ in second), a node will not occur at distance $x$. The value of $x$ is
$25\text{ cm}$
$62.5\text{ cm}$
$12.5\text{ cm}$
$37.5\text{ cm}$
Solution
Node will occur, when
$kx = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}$, etc. $\left(\because k = \frac{\pi}{25}\right)$
$\Rightarrow x = 12.5\text{ cm}, 37.5\text{ cm}, 62.5\text{ cm}$, etc.