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A sinusoidal wave travelling in the positive direction on a stretched string has amplitude 2.0 cm, wavelength 1.0 m and wave velocity 5.0 m/s. Ar x = 0 and t = 0, it is given that y=0 and (deltay)/(deltat)lt 0. Find the dr wave function y(x, t). |
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Answer» Solution :We start with a general form for a RIGHTWARD MOVING wave. `y(x,t) =A sin (kx - omegat + phi)`. The amplitude given is A= 2.0 cm=0.02 m. The wavelength is given as, `lambda`= 1.0m `:.` Wave number `k =(2pi)/lambda = 2pi m^(-1)` Angular frequency `omega =vk = 10pi` red /s `:. y (x,t) =(0.02) sin[2pi(x - 5.0t) +phi]` We are told that for x = 0, t = 0, Y= 0 and `(deltay)/(deltat) lt 0` From these conditions, we may conclude that `phi = 2 N pi` where n=0, 2, 4, 6, ....... THEREFORE, `y(x,t) = (0.02m) sin[(2pi m^(-1) ) x - (10pi s^(-1))t ] m` |
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