I am trying to learn one dimensional wave and how to calculate there frequency, speed and direction

Thread Starter

Sammy_g01

Joined May 15, 2020
1
So I have been trying to learn how to calculate frequency and speed of a wave. I have this following question which I am not sure how to answer. Can some one talk me through it please.
1589546267514.png
 

andrewmm

Joined Feb 25, 2011
323
You mean one dimension of amplitude, one of time .,..

if in doubt, put it into a spread sheet... ( thats what we used to do to "check" our home work... )
Down left, phase angle ( t ) , and amplitude( x ) , on right , the function sin( 20 pi t - 2 pi x )
 

MrChips

Joined Oct 2, 2009
21,126
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.
 

Papabravo

Joined Feb 24, 2006
13,728
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.
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.
 

MrChips

Joined Oct 2, 2009
21,126
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
 

Papabravo

Joined Feb 24, 2006
13,728
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
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.

The derivative should be a partial derivative since there are two variables involved.
 
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MrChips

Joined Oct 2, 2009
21,126
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).
 

Papabravo

Joined Feb 24, 2006
13,728
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).
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.

https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/02:_The_Classical_Wave_Equation/2.01:_The_One-Dimensional_Wave_Equation

The standing wave is what happens when you transmit into a near perfectly matched antenna. Very small return loss.
 

Delta prime

Joined Nov 15, 2019
336
The standing wave is what happens when you transmit into a near perfectly matched antenna. Very small return loss.
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
 

Papabravo

Joined Feb 24, 2006
13,728
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
Yup, that's the way I see it.
 

MrChips

Joined Oct 2, 2009
21,126
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.
 

Papabravo

Joined Feb 24, 2006
13,728
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.
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.
 

MrAl

Joined Jun 17, 2014
7,592
So I have been trying to learn how to calculate frequency and speed of a wave. I have this following question which I am not sure how to answer. Can some one talk me through it please.
View attachment 207249
Hello,

v(t,x) would be a function that describes the wave.

Here is a plot. Note that along 't' we see a sine wave as expected, but we also see a sine wave along 'x'. The one along 'x' is of lower frequency than the one along 't'. But what is happening is the wave changes amplitude as 'x' changes (advances in space) while the wave also changes in time. So the idea would be to look at one place along 'x' (say x=0.6) and one point in time 't' (say t=0.1) and that will have a particular amplitude. Then if you move along 'x' the amplitude will either go up or down, and as you change the time the wave will change amplitude also. A somewhat interesting idea is that you might actually be able to find a path though the mapping where the amplitude is constant when you change both x and t in a certain way.
Probably the main point though is that if you were to stand at that point on 'x' where x=0.6 you would see the wave change according to 't', and if you move left or right you'd see the phase change. This is an important point such as in a transmission line.
If you look along the 'x' axis in the drawing you can see the sine wave along 'x', and if you look along the 't' axis you can see the faster sine wave.

Wave_20200521_021718.gif
 
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