It does. To see it you have to do two sketches, the first at t=0 and the second at t=0.5 on the interval [-2, 6]. Even then it may not be apparent what is going on.What do you mean by "speed and direction of travel of the wave"?
I am not aware of a sine wave having a speed and direction unless it is a travelling wave in a medium, in which case you have provided no information in order to determine speed and direction.
At any point x on the one dimensional number line and at any point t in time the angle is defined by the expression (2π20t - 2πx), on the interval from 0 to 2π. The expression is zero everywhere else. What you have is sin (θ(x, t)). This depends on both time and position in space. It is a 1-dimensional traveling wave and is a solution to the 1-dimensional wave equation. The specific case we are talking about is where θ is a function of (x + ct) or (x - ct). One is a traveling wave in the positive x direction and the other is a traveling wave in the minus x direction. The constant c, is the speed of the traveling wave. In the limit as c approaches 0, it turns into a standing wave.I still don't get it.
When I see
y = sin(θ)
θ is an angle.
Where does speed and direction come in? The only velocity I can see is angular velocity, ω = dθ/dt
I used c for the velocity, because in most of my work the waves traveled at the S.O.L. Here is a web page with some animations that might help visualize what is going on.Ok, I get it now. I was not familiar with the wave notation.
So x is a position is space and one can observe the phase change along the direction of x.
I suppose one has to assume that t is a dimension in time and x is a linear dimension in space, and to me v stands for voltage (this is AAC, remember). Good to know this. At least I think I know what π is. (tongue in cheek).
That's the way I like it no return loss .The standing wave is what happens when you transmit into a near perfectly matched antenna. Very small return loss.
Yup, that's the way I see it.That's the way I like it no return loss .
Issues arise when power is transferred into the transmission line or feeder and it travels towards the load. If there is a mismatch, i.e. the load impedance does not match that of the transmission line, then it is not possible for all the power to be transferred.
the power that is not transferred into the load has to go somewhere and there it travels back along the transmission line back towards the source
The resulting VSWR is normally expressed as a ratio, e.g. 2:1, 5:1, etc. A perfect match is 1:1 and a complete mismatch, i.e. a short or open circuit is ∞:1
I think you have the sense of it. Much harder for the fans to perform a standing wave, but I bet with practice it could be done.Oh, why did I not see this before? I now see that this is an optical illusion.
A perfect example is the wave across the ball stadium. Each ballgame fan stands up and sits down exactly where they are sitting. Nobody moves laterally. There is a phase shift (or delay) proportional to the seating position x. What actually "moves" is the information across the stadium. So the speed is the position as a function of the phase shift and time interval.
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