A transverse wave is represented by the equationy=y0sin2πλ(vt−x)For what value of λ, the maximum particle velocity equal to two times the wave velocity

On comparing the given equation with standard equation y=asin2πλ(vt−x). It is clear that wave speed (v)wave=v and maximum particle velocity (vmax)particle=aω=y0× co-efficient of t=y0×2πvλ ∵   (vmax)particle=2(ω)wave⇒a×2πvλ=2v⇒λ=πy0