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)

$\left[\begin{array}{cc}x=0is& aNode\\ \frac{\partial y}{\partial x}=0at& t=0\end{array}\right]\Rightarrow y=Asinkx.sin\omega t$
$\frac{\partial y}{\partial x}=Ak\cdot coskx\cdot sin\omega t$

$\omega \cdot 2T=2\pi$
$T=\frac{\pi }{\omega }$
$T^{\prime }=\frac{2\pi }{\omega }=2T$