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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2024 · 4 April · Morning Shift · Physics · Units and Dimensions

The equation of stationary wave is : y=2 a ((2 π n t)/(λ)) ((2 π...

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

Options

  1. AThe dimensions of n/λn / \lambda is [T]
  2. BThe dimensions of n\mathrm{n} is [LT−1]\left[\mathrm{LT}^{-1}\right]
  3. CThe dimensions of xx is [L]
  4. DThe dimensions of nt\mathrm{nt} is [L]

Correct answer

A. The dimensions of n/λn / \lambda is [T]

Step-by-step solution

Comparing the given equation with standard equation of standing 2πnλ=ω&2πλ=k\frac{2 \pi n}{\lambda}=\omega \& \frac{2 \pi}{\lambda}=k[nλ]=[ω]=T−1[nt]=[λ]=L[n]=[λω]=LT−1[x]=[λ]=L\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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