K-sol - Chapter K - Problems Blinn College - Physics 2425 -...

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Chapter K - Problems Blinn College - Physics 2425 - Terry Honan Problem K.1 Consider a pulse that in SI units has the shape u = f H x L = 8 x 2 + 4 . Write this as a function u H x , t L that describes this pulse moving in the positive x direction with a speed of 3 m ê s . Solution to K.1 A pulse of shape u = f H x L moving in the positive x-direction with speed v takes the form: u = f H x - v t L . Using this form of f H x L with v = 3 m ê s gives: f H x L = 8 x 2 + 4 ï u = 8 H x - 3 t L 2 + 4 . Problem K.2 What are the speed and direction of a pulse on a string that (in SI units) has the form: y H x , t L = 0.04 e - J x + 0.03 t 0.06 N 2 . Solution to K.2 A wave of the form: y H x , t L = f H x ° v t L represents a pulse of shape y = f H x L moving in the ± x direction with speed v . Here we have y H x , t L = 0.04 e - H x ê 0.06 L 2 with v = 0.03 m ê s moving in the negative x direction. Problem K.3 A sinusoidal pulse on a string has the mathematical form y H x , t L = H 0.80 m L sin B 2 p 10 H x - 4 t LF . Plot the y vs. x graph at t = 0 s. By the time t = 0.6 s how much has the pulse shifted. On the same graph plot y vs. x at t = 0.6 s. Solution to K.3 After t = 0.6 s the graph has shifted by v t = 4 μ 0.6 = 2.4 m.
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5 10 15 20 x H m L - 0.75 - 0.5 - 0.25 0.25 0.5 0.75 y H m L Problem K.4 A string with a linear density of m = 4 μ 10 - 3 kg ê m is given a tension of 360 N. What is the speed of waves on this string? Solution to K.4
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K-sol - Chapter K - Problems Blinn College - Physics 2425 -...

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