The equation of stationary wave is: y = 2asin ((2)/(λ))cos ((2π x)/(λ)). Which of the following is NOT correct: (a) The dimensions of nt is [L] (b) The dimensions of n is [LT⁻¹] (c) The dimensions of x is [L] (d) The dimensions of n/λ is [T]

Answer: (d). Arguments of sine and cosine are dimensionless. 2π nt/λ dimensionless ⇒ [nt] = [L], [n] = [LT⁻¹]: (a), (b) correct. 2π x/λ dimensionless ⇒ [x] = [L]: (c) correct. [n/λ] = [LT⁻¹]/[L] = [T⁻¹], not [T]. So the answer is (d).

The equation of stationary wave is: y = 2asin ((2)/(λ))cos ((2π… | JEE Main 2024 (4 Apr, Shift 1)

Q21JEE Main 2024 · 4 APR · SHIFT 1Easy

Applications of Dimensional Analysis

The equation of stationary wave is:

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

Which of the following is NOT correct:

Show answer and solution

Answer: (d)

Arguments of sine and cosine are dimensionless.
$2\pi nt/\lambda$ dimensionless $\Rightarrow [nt] = [L]$ , $[n] = [LT^{-1}]$ : (a), (b) correct.
$2\pi x/\lambda$ dimensionless $\Rightarrow [x] = [L]$ : (c) correct.
$[n/\lambda] = [LT^{-1}]/[L] = [T^{-1}]$ , not $[T]$ .
So the answer is (d).

Report a mistake

Applications of Dimensional Analysis question from JEE Main 2024 (4 Apr, Shift 1)

More questions on Applications of Dimensional Analysis