Question

The equation $y=5\sin \left(\frac{\pi x}{25}\right)\cos \left(450t\right)$ represent the stationary wave setup in a vibrating sonometer wire,where x,y are in cm and t is second.The distance of second and third nodes from one end are

• A. $50,75$
• B. $25,50$
• C. $15,50$
• D. $20,50$

Answer 1

The correct option is B $25,50$

$y=5\sin \left(\frac{\pi x}{25}\right)\cos \left(450t\right)$
$\frac{\pi x}{25}=0,\pi ,2\pi ,3\pi ,....$
For $2nd$ & $3rd$ node
$\frac{\pi x}{25}=\pi$
$x=25cm$
and
$\frac{\pi x}{25}=2\pi$
$x=50cm$
$\therefore 2nd$ is at $25cm$
and
$3rd$ node is at $50cm$