A pulse travelling on a string is represented by the function Y = a^3/((x-vt)^2+a^2 ). Where a = 5 mm and v = 20 cm s-1. Sketch the shape of the string at t = 0, 1 s and 2 s. Take x = 0 in the middle of the string.

Sol. The pulse is given by, y = [(a3) / {(x – vt)2 + a2}] a = 5 mm = 0.5 cm, v = 20 cm/s At t = 0s, y = a3 / (x2 + a2) The graph between y and x can be plotted by taking different values of x. (left as exercise for the student) similarly, at t = 1 s, y = a3 / {(x – v)2 + a2} and at t = 2 s, y = a3 / {(x – 2v)2 + a2}