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Phys 2214 hw3 Solutions

# Phys 2214 hw3 Solutions - Phys 2214 Homework#3 Solutions 1...

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Phys 2214 Homework #3 Solutions September 15, 2011 1. The disturbance travels down the rubber tube with the wave speed, which, for a one-dimensional transverse wave with constant tension and mass/length, is given by v = s τ μ . The tension τ is equal to the weight of the mass hanging over the pulley, which is 10 kg × 9 . 8 m/s 2 = 98 N . The linear density μ = 0 . 5 kg/ 10 m = 0 . 05 kg/m . Then v = 44 . 3 m/s and the time to travel down the rubber tube is t = L/v = 10 m/ 44 . 3 m/s = 0 . 23 s . 2. the transverse wave is given by y ( x, t ) = 0 . 01 m cos 20 rad m x - 2000 rad s t ! . (a) See the figure below, which is a plot of y ( x ). According to the Pulse Equation, the velocity of the particles in the medium is related to the spatial slope of the wave: ∂y ∂t = - v ∂y ∂x , where the minus sign is used for waves moving in the + x direction. So, for (A), the maximum upward particle velocity takes place where the slope of the wave is the most negative (see the plot). For (B), the particle velocity is zero whenever the slope of the wave is zero (see the plot). For (C), using the wave equation gives the 1

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