$y=A \sin (\omega t-k x)$

Wave velocity, $v=\frac{\omega}{k}$                                 $...(i)$

Particle velocity, $v_{p}=\frac{d y}{d t}=A \omega \cos (\omega t-k x)$

Maximum particle velocity, $\left(v_{p}\right)_{\max }=A \omega$         $...(ii)$

According to the given question

${v=\left(v_{p}\right)_{\max }}$

${\frac{\omega}{k}=A \omega}$                  $(Using\,(i)\,and\,(ii))$

$\frac{1}{k}=A \quad$ or $\quad \frac{\lambda}{2 \pi}=A \quad\left(\because \quad k=\frac{2 \pi}{\lambda}\right)$

$\lambda=2 \pi A$