Hence, the maximum particle velocity $=\pm A \omega$ which is at the mean position.

From the given equation of wave$:$

$y=A \sin \left(2 \pi f t-2 \pi \frac{x}{\lambda}\right)$

From the wave equation, $\omega=2 \pi f$

and wave velocity, $v=\frac{\omega}{k}=\frac{2 \pi f}{\frac{2 \pi}{\lambda}}$

$v=\lambda f$

From the given condition$:$

$A \times 2 \pi f=4 \lambda f$

$\lambda=\frac{\pi A}{2}$