Equation of stationary wave is mathrm{y}=2 mathrm{a} sin left(frac{2 π mathrm{nt}}{λ}right) cos le

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1.Units, Dimensions and Measurement

hard

The equation of stationary wave is

$\mathrm{y}=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}\right)$

Which of the following is NOT correct

A

The dimensions of nt is $[L]$

B

The dimensions of $n$ is $\left[\mathrm{LT}^{-1}\right]$

C

The dimensions of $n / \lambda$ is $[T]$

D

The dimensions of $x$ is $[L]$

(JEE MAIN-2024)

Solution

Comparing the given equation with standard equation of standing $\frac{2 \pi \mathrm{n}}{\lambda}=\omega \& \frac{2 \pi}{\lambda}=\mathrm{k}$

${\left[\frac{\mathrm{n}}{\lambda}\right]=[\omega]=\mathrm{T}^{-1}}$

${[\mathrm{nt}]=[\lambda]=\mathrm{L}}$

${[\mathrm{n}]=[\lambda \omega]=\mathrm{LT}^{-1}}$

${[\mathrm{x}]=[\lambda]=\mathrm{L}}$

Hence option $(3)$

Standard 11

Physics

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