Progressive Wave Equation question from MHT CET 2025 (23 Apr, Shift 1)

Answer: (c)

1. Maximum particle velocity $v = A\omega$; wave velocity $V = \frac{\omega}{k} = \frac{\omega\lambda}{2\pi}$.
2. $\frac{v}{V} = \frac{A\omega}{\omega\lambda/2\pi} = \frac{2\pi A}{\lambda}$
3. So the answer is (c) $v = \frac{2\pi A}{\lambda}V$.