The equation of stationary wave is : $y=2 a \sin \left(\frac{2 \pi n t}{\lambda}\right) \cos \left(\frac{2 \pi x}{\lambda}\right)$ Which of the following is NOT correct

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

(A) The dimensions of nt is [L]

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

(D) The dimensions of $x$ is $[L]$

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Waves & Sound

The equation of stationary wave is :

y = 2 a sin (\frac{2 π n t}{λ}) cos (\frac{2 π x}{λ})

Which of the following is NOT correct

Answer: (C)

Comparing

y = 2 a sin (\frac{2 π n t}{λ}) cos (\frac{2 π x}{λ})

with the standard standing wave, the arguments must be dimensionless.

[\frac{n t}{λ}]

dimensionless

\Rightarrow [n t] = [λ] = L

— (A) correct.

[n] = \frac{[ λ ]}{[ t ]} = \frac{L}{T} = L T^{- 1}

— (B) correct.

[x] = [λ] = L

— (D) correct.

[\frac{n}{λ}] = \frac{L T ^{- 1}}{L} = T^{- 1}

, not

[T]

— (C) is wrong.

The question asks which is NOT correct

\Rightarrow

option C.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Single correct option