A transverse wave is represented by y=y0sin2πλvt−x. For what value of  λ is the maximum particle velocity equal to twice the wave velocity?

Given  y=y0sin2πλvt−xω=2πλv,k=2πλVelocity of wave Vω=vVelocity of particle  VP=∂y∂t=y02πvλcos2πλ(vt−x)Maximum velocity of particle  Vmax=2πvy0λgiven that  Vmax=2Vwave∴2πvy0λ=2v∴λ=πy0Therefore, the correct answer is ( D )