A simple harmonic progressive wave is given by the equation y = asin 2π(nt - (x)/(λ)). If the wave velocity is equal to 1/6 × (maximum particle velocity), then the wavelength λ is a = amplitude, n = frequency, t = time, y = displacement, x = distance (a) (π a)/(2) (b) (π a)/(3) (c) (3π a)/(2) (d) (2π a)/(3)

Answer: (b). Wave velocity v = nλ; maximum particle velocity = aω = 2π n a nλ = 1/6(2π n a) ⇒ λ = (π a)/(3) So the answer is (b) (π a)/(3).

A simple harmonic progressive wave is given by the equation y = asin… | MHT CET 2026 (12 May, Shift 1)

Q22MHT CET 2026 · 12 MAY · SHIFT 1Medium

Progressive Wave Equation

A simple harmonic progressive wave is given by the equation $y = a\sin 2\pi\left(nt - \frac{x}{\lambda}\right)$ . If the wave velocity is equal to $\frac{1}{6} \times$ (maximum particle velocity), then the wavelength $\lambda$ is $\{a =$ amplitude, $n =$ frequency, $t =$ time, $y =$ displacement, $x =$ distance $\}$

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Answer: (b)

Wave velocity $v = n\lambda$ ; maximum particle velocity $= a\omega = 2\pi n a$
$n\lambda = \frac{1}{6}(2\pi n a) \Rightarrow \lambda = \frac{\pi a}{3}$
So the answer is (b) $\frac{\pi a}{3}$ .

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Progressive Wave Equation question from MHT CET 2026 (12 May, Shift 1)

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