Question

A travelling harmonic wave on a string is described by : y = 7.5 sin (0.0050 x + 12t + π/4)

(a) What are the displacement and velocity of oscillation of a point at x = 1 cm and t = 1 a ? Is this speed equal to the speed 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 = 2 s, 5 s, 11 s.

Answer 1

The general equation of the travelling harmonic wave (travelling towards left) is

(Negative sign has been taken as the wave travels towards left) We thus find that v_p (particle speed) is not equal to v (wave speed*)

All points located at distances, x = nλ (where n = ± 1, ± 2, ± 3, ...) from the point x = 1 cm have the same displacement and velocity.