An apparatus similar to the one used in lab uses an oscillating motor at one end

Question

An apparatus similar to the one used in lab uses an oscillating motor at one end to vibrate a long rope with frequency f = 40.0 Hz and amplitude A = 0.25 m. The rope is held at constant tension by hanging a mass on the other end. The rope has mass denstiy ? = 0.02 kg/m, and tension T = 20.48 N. Assume that at t = 0 the end of the rope at x = 0 has zero y-displacement and is moving downward. What is the y-displacement of the piece of rope at x1 = 0.5 m when t = 0.0? What it's asking for is... y1 = ??? ... if it helps here is an image url to an image associated with the problem: https://www.smartphysics.com/Content/Media/Images/Mechanics/24/stringwave.gif

Explanation / Answer

here ,A = 0.25 m , f = 40 Hz , u = 0.02 kg/m , T = 20.48 N wave speed (v) = sqrt ( T / u ) on solving , v = 32 m/s For, y (x,t) = A* sin(w*t - k*x) w = 2*pi*f therefore, w= 251.38 rad/s since wave speed (v) = w / k therefore , k = 7.85 rad/m on substituting , y(x,t) = 0.25* sin ( 251.38*t - 7.85 *x )

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