Question

A wave is travelling towards positive $x-$axis. Its equation is given by,
$y=2\sin \left(2\pi \right(5x-3t\left)\right)$
Where, $y_1,x$ are in $\text{cm}$.
What is the velocity of the particles of the medium, at, $x=\frac{1}{4}\text{cm and}t=\frac{1}{4}\text{sec}$?

• A. $24\pi \text{cm/s}$
• B. $12\pi \text{cm/s}$
• C. $16\pi \text{cm/s}$
• D. $6\pi \text{cm/s}$

Answer 1

The correct option is B $12\pi \text{cm/s}$

Given equation of wave is,

$y=2\sin \left(2\pi \right(5x-3t\left)\right)$

The velocity of a particle is, $V_p=\frac{\partial y}{\partial t}=2\times -3\times 2\pi \cos 2\pi (5x-3t)$

At, $x=\frac{1}{4}\text{cm and}t=\frac{1}{4}\text{sec}$

$V_p=-12\pi \cos \left[2\pi (\frac{5}{4}-\frac{3}{4})\right]$
$=-12\pi \cos \pi =12\pi \text{cm/s}$

Hence, $\left(B\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question ?}\\ \text{This question gives you concept of phase and its calculation in wave.}\end{array}$