It is clear that wave speed ${(v)_{wave}} = v$ and maximum particle velocity

${({v_{\max }})_{particle}} = a\omega = {y_0} \times $ co-efficient of $t  = {y_0} \times \frac{{2\pi v}}{\lambda }$

${({v_{\max }})_{particle}} = 2 (\omega)_{wave}$ ==> $\frac{{a \times 2\pi v}}{\lambda } = 2v$ ==> $\lambda = \pi {y_0}$