Problem 2 Traveling Wave Pulse - Universe Physics: Quantum Physics | PHYS 214, Assignments of Quantum Physics

Download Problem 2 Traveling Wave Pulse - Universe Physics: Quantum Physics | PHYS 214 and more Assignments Quantum Physics in PDF only on Docsity! Physics 214 Problem 2 Week 1 Traveling Wave Pulse A voltage pulse travels down a coaxial cable in the +x direction at a speed of v = 2.5 × 108 m/s. At time t = 0 the potential difference between the inner conducting wire and the outer conducting shell is given by this formula,V (x) = V0e −αx2 , where Vo = 0.7 volts and α = 2 m-2. (Note: αx2 is dimensionless.) a) On the axes below, sketch V(x) versus x showing the shape of the pulse at time t = 0 s. (Hint: For what values of x does the curve fall to 1/e of its maximum value? xe = ±0.707m) With a dashed curve, sketch the pulse at a time 4 nanoseconds later. At t = 4 ns, the maximum potential occurs at what value of x? xmax = vt = 1 m. b) Give a formula for the new function V(x) that describes the pulse at t = 4 ns. c) Write a formula for V(x,t) that describes the pulse as a function of position and time. (You may use v for velocity.) d) What formula would describe the pulse if it were going in the opposite direction? x Vo V (Volts) x (m) -2 2 1 0 -1 21 )mx( oeV)x(V −−= α 2)vtx( oeV)t,x(V −−= α 2)vtx( oeV)x(V +−= α Solution