The equation of a wave travelling on a string stretched along the X-axis is given by Y = A e^(-(x/a+t/T)^2 ). a) Write the dimensions of A, a and T. (b) Find the wave speed. (c) In which direction is the wave travelling? (d) Where is the maximum of the pulse located at t = T? At t = 2T?

Sol . Given y = Ae-[(x / a)+(t / T)]^2 a) [A] = [M0L1T0], [T] = [M0L0T1] [a] = [M0L1T0] b) Wave speed, v = λ/T = a/T [Wave length λ = a] c) If y = f(t – x/v) → wave is traveling in positive direction and if y = f( t + x/v) → wave is traveling in negative direction so, Y = Ae-[(x / a)+(t / T)]^2 = Ae-(1/T)[x/a/T +t]^2 = Ae-(1/T)[x/a/T +t]^2 i.e. y = f{t + (x / v)}