The equation of stationary wave is : $y=2 a \sin \left(\frac{2 \pi n t}{\lambda}\right) \cos \left(\frac{2…
The equation of stationary wave is :
$y=2 a \sin \left(\frac{2 \pi n t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right) \text {. }$
Which of the following is NOT correct :
The dimensions of $n / \lambda$ is [T]
The dimensions of $\mathrm{n}$ is $\left[\mathrm{LT}^{-1}\right]$
The dimensions of $x$ is [L]
The dimensions of $\mathrm{nt}$ is [L]
Solution
Comparing the given equation with standard equation of standing $\frac{2 \pi n}{\lambda}=\omega \& \frac{2 \pi}{\lambda}=k$
$\begin{aligned}
& {\left[\frac{\mathrm{n}}{\lambda}\right]=[\omega]=\mathrm{T}^{-1}} \\
& {[\mathrm{nt}]=[\lambda]=\mathrm{L}} \\
& {[\mathrm{n}]=[\lambda \omega]=\mathrm{LT}^{-1}} \\
& {[\mathrm{x}]=[\lambda]=\mathrm{L}}
\end{aligned}$