Progressive Wave Equation question from MHT CET 2023 (9 May, Shift 2)

Answer: (b)

1. $y = a\sin(2\pi b t - 2\pi c x)$: $v_{p,\max} = 2\pi b a$, wave velocity $v = \frac{2\pi b}{2\pi c} = \frac{b}{c}$
2. $2\pi b a = \frac{1}{2}\cdot\frac{b}{c} \Rightarrow c = \frac{1}{4\pi a}$
3. So the answer is (b) $\frac{1}{4\pi a}$.