A transverse wave is described by the equation Y=Y0sin⁡2π(ft−x/λ) The maximum particle velocity is equal to four times the wave velocity if

v=dYdt=Y0cos⁡2πft−xλ×2πf or V=2πfY0cos⁡2πft−xλ The particle velocity is maximum, when cos⁡2πft−xλ=1 Vmax=2πfY0 We know thatY = qsin (rot -k x The wave velocity V is given bY V=ωk=2πf2π/λ=fλ  Given that vmax=4V ∴ 2πfY0=4fλ  or  λ=πY02