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Think of a train carrying sinusoids. Each flatcar carries one sinusoid having length l. If the train is not moving, the phase at any point x is:. If the train is moving:. Phase velocity : the velocity of a point of constant phase on the traveling waveform. -. +. x = 0.
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Think of a train carrying sinusoids. Each flatcar carries one sinusoid having length l. If the train is not moving, the phase at any point x is: If the train is moving: Phase velocity: the velocity of a point of constant phase on the traveling waveform. - + x = 0
Consider the position x = 0. At time , the point on the train passing x = 0 will be the point on the train which was at when t = 0. The phase associated with that point is : - + x = 0
Our choice for the position of the origin, x = 0, was totally arbitrary!! Any of these forms are valid for expressing a traveling wave moving in the positive x direction! - + x = 0
For traveling waves moving in the negative x direction, the sign on one of the terms of the phase expression must be reversed:
The Cowboy Way A real cowboy uses complex exponentials. The preferred form for voltage waveforms is: … for traveling waves moving in the positive x direction. … for traveling waves moving in the negative x direction. Complex constants representing the magnitudes and reference phases of the traveling waves.
Train Station How many cars are in the station at any time? S You Each car coming out is exactly NS cars ahead of each car going in. What do you see, standing at the station entrance? x = xs Dxs You see each car coming out exactly nS (the fractional part ofNS)cars ahead of each car going in. DS = -2Dxs The phase lead of the sinusoid coming out with respect to the phase of the sinusoid going in is equal to two pi times nS. What has changed? Only the observer’s position!
Voltage Minima Voltage Maxima
