Units & Dimensions

JEE Main level, single correct, medium

60 of 149

Question 60 of 149

The equation of stationary wave is :
y=2asin⁡(2πntλ)cos⁡(2πxλ). 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 :

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Answer: (A) The dimensions of n/λn / \lambda is [T]

Comparing the given equation with standard equation of standing 2πnλ=ω&2πλ=k\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}$

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