The equation of a wave is y = 0.07sin (12π x - 3000π t) where x is in metre and t is in second then 1 m m (a) λ = m, v = 250 (b) a = 0.07 m, v = 500 6 s s m 1 m (c) n = 1500 Hz, v = 200 (d) λ = m, v = 500 s 3 s

Answer: (a). Compare with y = Asin (kx - ω t): A = 0.07 m, k = 12π, ω = 3000π. λ = 2π/k = (2π)/(12π) = 1/6 m, n = (ω)/(2π) = 1500 Hz v = (ω)/(k) = (3000π)/(12π) = 250 m/s So the answer is (a) λ = 1/6 m, v = 250 m/s.

The equation of a wave is y = 0.07sin (12π x - 3000π t) where x is in… | MHT CET 2026 (15 May, Shift 1)

Q1MHT CET 2026 · 15 MAY · SHIFT 1Easy

Progressive Wave Equation

The equation of a wave is $y = 0.07\sin(12\pi x - 3000\pi t)$ where $x$ is in metre and $t$ is in second then $1$ m m

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Answer: (a)

Compare with $y = A\sin(kx - \omega t)$ : $A = 0.07\text{ m}$ , $k = 12\pi$ , $\omega = 3000\pi$ .
$\lambda = \dfrac{2\pi}{k} = \dfrac{2\pi}{12\pi} = \dfrac{1}{6}\text{ m}$ , $n = \dfrac{\omega}{2\pi} = 1500\text{ Hz}$
$v = \dfrac{\omega}{k} = \dfrac{3000\pi}{12\pi} = 250\text{ m/s}$
So the answer is (a) $\lambda = \dfrac{1}{6}\text{ m}$ , $v = 250\text{ m/s}$ .

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