6hw6 - Physics 315 Oscillations and Waves Homework 6 Due in...

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Unformatted text preview: Physics 315: Oscillations and Waves Homework 6: Due in class on Wednesday, Oct. 28th 1. Write the traveling wave ψ ( x, t ) = A cos( k x − ω t ) as a superposition of two standing waves. Write the standing wave ψ ( x, t ) = A cos( k x ) cos( ω t ) as a superposition of two traveling waves propagating in opposite directions. Show that the following superposition of traveling waves, ψ ( x, t ) = A cos( k x − ω t ) + A R cos( k x + ω t ) , can be written as the following superposition of standing waves, ψ ( x, t ) = A (1 + R ) cos( k x ) cos( ω t ) + A (1 − R ) sin( k x ) sin( ω t ) . 2. A transmission line of characteristic impedance Z occupies the region x < 0, and is terminated at x = 0. Suppose that the current carried by the line takes the form I ( x, t ) = I i cos( k x − ω t ) + I r cos( k x + ω t ) for x ≤ 0, where I i is the amplitude of the incident signal, and I r the amplitude of the signal reflected at the end of the line. Let the end of the line be open circuited...
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6hw6 - Physics 315 Oscillations and Waves Homework 6 Due in...

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