Question

A stationary wave of amplitude $A$ is generated between the two fixed ends $x=0$ and $x=L$ . The particle at $x=\frac{L}{3}$ is a node. There are only two particles between $x=\frac{L}{6}$ and $x=\frac{L}{3}$ which have maximum speed half of the maximum speed of the anti-node. Again there are only two particles between $x=0$ and $x=\frac{L}{6}$ which have maximum speed half of that at the antinodes. The slope of the wave function at $x=\frac{L}{3}$ changes with respect to time according to the graph shown. The symbols $\mu $ , $\omega $ and $A$ are having their usual meanings if used in calculations.



The time period of oscillations of a particle is

• A. $T$
• B. $2T$
• C. $\frac{T}{2}$
• D. $4T$

Answer 1

Answer: (B)

$\begin{bmatrix} x=0 \, is & a \, Node \\ \frac{\partial y}{\partial x}=0 \, at & t=0 \end{bmatrix} \, \Rightarrow y=Asin kx.sin⁡ωt$
$\frac{\partial y}{\partial x}= \, Ak\cdot cos kx\cdot sin⁡ωt$

$\omega \cdot 2T=2\pi $
$T=\frac{\pi }{\omega }$
$T'=\frac{2 \pi }{\omega }=2T$