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A sinusoidal wave trsvelling in the positive direction on a stretched string has amplitude `2.0 cm`, wavelength `1.0 cm` and velocity `5.0 m//s`. At `x = 0` and ` t= 0` it is given that `y = 0` and `(dely)/(delt) lt 0`. Find the wave function `y (x, t)`. |
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Answer» Correct Answer - A::B::D We start with a general equation for a rightward moving wave, `y(x, t) = A sin (kx - omegat + Phi) ` The ampitude given is `A = 2.0 cm = 0.02 m` A wavelength is given as `lambda = 1.0 m` :. Angular wave number, `k =(2pi)/( lambda) = (2pi) m^(-1)` Angular frequency, `omega = vk = (10pi) rad//s` ` :. y(x, t) = (0.02) sin [ 2pi (x - 5.0t) + Phi]` We are given that for `x = 0`, `t = 0`, `y =0` and `(dely)/(delt) lt 0` i.e. `0.02 sin Phi = 0` (as `y = 0`) and `-0.2 pi cos Phi lt 0` From these conditions, we conclude that ` Phi = 2npi` , where `n = 0,2,4,6`...... Therefore, `y(x, t) = (0.02 m) sin [(2pi m^(-1)) x - (10pi rad s^(-1)) t] m` |
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