A travelling wave on a string is given by y=7.5sin(0.005x+12t+π/4) . Find the displacement and velocity of the particle at a point x=1 cm  t=1sec  . Take sin(12.7o)=0.22  .

Given  y=7.5sin0.005x+12t+π/4→(i) Putting x=1cm  and t=1sec in eq (i) we have y=7.5sin0.005×1+12×1+3.1424 =7.5sin12.79 rad =7.5sin732.70      π rad=1800 =7.5sin4π+12.70 =7.5sin12.70 =7.5×0.22=1.65​cm  Particle velocity is obtained by differentiating (i) w.r.t time t v=dy/dt=7.5×12×cos0.005x+12t+π/4  Putting x=1cm and  t=1sec v=7.5×12×cos(12.70)=87.8 cm/sec