Q 11-01-093JEE MainJEE Main 2024 (4 Apr, Shift 1)Easy
The equation of a stationary wave is $y = 2a\sin\left(\dfrac{2\pi nt}{\lambda}\right)\cos\left(\dfrac{2\pi x}{\lambda}\right)$. Which of the following is NOT correct?
Answer: (A) The dimensions of $n/\lambda$ is $[\text{T}]$
The arguments of sine and cosine are dimensionless.
From $\dfrac{2\pi x}{\lambda}$: $[x] = [\lambda] = [\text{L}]$.
From $\dfrac{2\pi nt}{\lambda}$: $[nt] = [\text{L}]$, so $[n] = [\text{L}\text{T}^{-1}]$ and $\left[\dfrac{n}{\lambda}\right] = [\text{T}^{-1}]$, not $[\text{T}]$.
So option (A) is not correct.
Solution by Sreeraj P, M.Sc Physics