Given, Amplitude of the wave = A
Maximum velocity of particle V_max = 4v
                           (where v is the velocity of wave)
Maximum velocity of wave, v_max = 4v

or            ${\text{v}}_{\text{max}}=\text{A}\omega =4\text{v}$

$\therefore \omega =\frac{4\text{V}}{\text{A}}$

Wavelength of the wave,

$\lambda =\frac{\text{velocity of wave (v)}}{\text{frequency of wave (f)}}=\frac{\text{v}}{\omega }=\frac{2\pi \text{v}}{\omega }$

   $=\frac{2\pi \text{v}}{4\text{v}/\text{A}}=\frac{\pi \text{A}}{2}$     ....(where, $\text{f}=\frac{\omega }{2\pi }$)