A simple harmonic progressive wave is given by Y = Y₀sin 2π(nt - (x)/(λ)). If the wave velocity is (1/8) th the maximum particle velocity then the wavelength is (a) (π Y₀)/(2) (b) (π Y₀)/(4) (c) (π Y₀)/(8) (d) (π Y₀)/(16)

Answer: (b). Wave velocity v = nλ; maximum particle velocity = 2π n Y₀ nλ = 1/8(2π n Y₀) ⇒ λ = (π Y₀)/(4) So the answer is (b) (π Y₀)/(4).

A simple harmonic progressive wave is given by Y = Y₀sin 2π(nt -… | MHT CET 2021 (21 Sep, Shift 1)

Q75MHT CET 2021 · 21 SEP · SHIFT 1Medium

Progressive Wave Equation

A simple harmonic progressive wave is given by $Y = Y_0\sin 2\pi\left(nt - \frac{x}{\lambda}\right)$ . If the wave velocity is $\left(\frac{1}{8}\right)$ th the maximum particle velocity then the wavelength is

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Answer: (b)

Wave velocity $v = n\lambda$ ; maximum particle velocity $= 2\pi n Y_0$
$n\lambda = \frac{1}{8}(2\pi n Y_0) \Rightarrow \lambda = \frac{\pi Y_0}{4}$
So the answer is (b) $\frac{\pi Y_0}{4}$ .

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Progressive Wave Equation question from MHT CET 2021 (21 Sep, Shift 1)

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