Question

The equation of standing wave in a stretched string is given by by y = 5sin($\frac{\pi x}{3}$) cos $\left(40\pi t\right)$, where x and y are in cm and t in second. The separation between two consecutive nodes is (in cm)

• A. 1.5
• B. 3
• C. 6
• D. 4

Answer 1

The correct option is B 3

$\begin{array}{c}y=5\sin \left(\frac{\pi x}{3}\right).\cos \left(4\pi t\right)\\ Hereinaboveequationk=\frac{\pi }{3}\\ \frac{2\pi }{\lambda }=\frac{\pi }{3}\\ \lambda =6cm\\ Hence,dis\tan cebetween2nodesis\frac{\lambda }{2}=3cm\end{array}$

Hence, the option $B$ is the correct answer.