Transwiki:Graphing vertical transverse waves

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The equation used to graph a vertical transverse wave, which rests apon a line segment medium, is as follows:

y=mx+b; ∑_(t >0)^∞▒〖t f(tsub1,tsub2,…)〗

An extension of ‘y = mx+b’, this is used to draw lines with crests and troughs, such as that of a transverse wave. T is the number of crests and troughs, and t-sub 1, t-sub 2, etc, are the lengths of each continual trough. For example, a line with a slope of 3 and a y-intercept of 2 that has 3 troughs and 4 crests, where the first crest–trough accompanies 1 unit, the second pair accompanies half a unit, and the third pair accompanies half a unit, and the last pair accompanies a full unit, is written like this:

Y = 3x + 2; 4 f[1, .5, .5, 1]

• The values that of said lengths of the trough–crest pairs MUST be equal to the slope. The slope, while obviously cannot pertain to a curved line, is used to represent the slope of the line that all the crests and troughs pass through. Let's look at the line we drew based on our numbers:

(Ignoring the green line) We can see that there are indeed four sets of crests and troughs, and that each line does encompass the length that we set, and that the added total length equals the slope of the Initial Line, or line that the crests and/or troughs branch off of. Which, in this case, is the red line. The purple line is the actually transverse wave. The green line is something I did in my spare time the night before this on this same MS Paint file.

Width of the Crest and/or Trough If the width of the crest or trough is to pass 1 unit, it is to be written as a side note in our equation, for example, using the same line we drew, if say the first crest or trough (the first being the one in the lowest value quadrant ) was to extend to 2 units in width, it would be written like this:

y=mx+b; ∑_(t >0)^∞▒〖t f(tsub1,tsub2,…)〗 [tsub1WID=2] In the event that multiple crests or troughs have width that goes beyond 1, it shall be written as such: y=mx+b; ∑_(t >0)^∞▒〖t f(tsub1,tsub2,…) 〗 [tsub1WID=2] ** [tsub2WID = 1.5] [tsub3WID = 1.2] …. In the case that the width of a crest or trough Is BELOW that of 1 unit, then it shall be written on the same format, but where we put “2” before, we would instead put a value below one, such as **.6 or 5/6.

• This is if the total line segment length is equal to one “Slope Unit,” which is the entire slope, or m/1. For example, a line segment with a slope of 2, that is only one slope unit in length, would go up ONLY from one unit to the right and two units up, which should look like this:

With a length of say, three slope units, a line with the same slope would look like this:

In the event that the line segment is equal to more than 1 slope unit, then the added lengths of the crests and troughs must be equal to the slope times the number of slope units.

• • These values are merely an example. The actual values depend on the wave.

[edit] Final observation

Here is an example of a more complex, and real transverse wave.

Y = 10x – 10; 4 f(1.5, .5, 2.5, 5.5)

The first and second crest–trough may look kind of weird, but the ones smaller in length usually do.

[edit] References