Question

A stretched string is vibrating according to the equation $y=5\sin \left(\frac{\pi x}{2}\right)\cos 4\pi t$, where $y$ and $x$ are in $\text{cm}$ and $t$ is in $\text{sec}$. The distance between two consecutive nodes on the string is

• A. $2\text{cm}$
• B. $4\text{cm}$
• C. $8\text{cm}$
• D. $16\text{cm}$

Answer 1

The correct option is A $2\text{cm}$

Given, equation of standing wave is
$y=5\sin \left(\frac{\pi x}{2}\right)\cos 4\pi t$
Compare the given equation with standard equation of standing wave.
$y=2A\sin kx\cos \omega t$
$k=\frac{2\pi }{\lambda }=\frac{\pi }{2}$
$\Rightarrow \lambda =4\text{cm}$
Hence, distance between two consecutive nodes is $\frac{\lambda }{2}=2\text{cm}$