Progressive Wave Equation question from MHT CET 2023 (11 May, Shift 2)

Answer: (d)

1. $y = A\sin(2\omega t - 2kx)$: maximum particle velocity $= 2\omega A$
2. Wave velocity $= \frac{2\omega}{2k} = \frac{\omega}{k}$
3. $2\omega A = \frac{\omega}{k} \Rightarrow A = \frac{1}{2k}$; with $k = \frac{2\pi}{\lambda}$, $A = \frac{\lambda}{4\pi}$
4. So the answer is (d) $\frac{\lambda}{4\pi}$.