When a wave travels in a medium, displacement of a particle is given by  y=asin⁡2π(bt−cx)  wherea, b and c are constants. The maximum particle velocity will be twice the wave velocity, if

Given,  y=asin⁡2π(bt−cx)On comparing this equation with general equationy=rsin⁡2πtT−2πλx, we get 2πT=ω=2πb,r=aλ=1c and T=1bMaximum particle velocity,  ωr=2πbaWave velocity,  v=λT=bcGiven, maximum particle velocity = 2 x wave velocity2πba=2×bc⇒c=1πa