the equation of transverse wave on a rope is y(x,t)=5sin(4.0t-0.02x) where (y) and(x) are measured in cm and (t) in second.calculate the maximum speed of particle on the rope

since, this is a plain progressive wave, therfore partivles are in S.H.M.;

so velocity of particle during S.H.M.=w(A^2-x^2);

which is maximum at x=0;

therefore maximum speed of particle=wA;

here, w=4; A=5;

so maximum speed of particle= 4 X 5 = 20 cm/sec