A travelling harmonic wave on a string is described by `y(x,t) = 7.5 sin (0.005 x + 12t+ pi//4)` (a) what are the displacement and velocity of oscillation of a point at x=1 cm, and t=1s? Is this velocity equal to the velocity of wave propagation?
(b) Locate the points of the string which have the same transverse displacements and velocity as the x=1 cm point at t=2s, 5s and 11s

Explanation

(a) 1.66 cm, `87.75 cm s^(-1)`, No, the velocity of wave propagation is `-24ms^(-1)`
(b) All points at distance of `n lamda (n = +- 1, +-2, +-3..)` where `lamda= 12.6m` from the point x=1 cm