Question

The equation of a stationary wave is $Y=10\sin \frac{\pi x}{4}\cos 20\pi t$. The distance between two consecutive nodes in meters is -

• A. 4
• B. 2
• C. 5
• D. 8

Answer 1

The correct option is A 4

$Y=10\sin \frac{\pi x}{4}\cos \pi t$

At nodles amplitude part is zero.

$\begin{array}{c}\Rightarrow 10\sin \frac{\pi x}{4}=0\\ \Rightarrow \frac{\pi x}{4}=0,\pi ,2\pi \\ \Rightarrow x=0.x=4,x=8\end{array}$

$\therefore 4$ is distance between two consultative node.

$\therefore$ Option $A$ is correct.