Graph Question?

Question

Can someone graph y= sin x + .05 sin (50x) please. Once it is graphed, zoom in a please tell me what that is.?

Can someone graph y= sin x + .05 sin (50x) please. Once it is graphed, zoom in a please tell me what the smaller wavy lines are?

Answer 1

You have two sine curves superimposed on each other. The main curve, y = sin x, is a regular wave with amplitude 1 and period 2 pi.

The second, smaller and curvier, is superimposed on top of it. These are your little wavy lines. This second curve has the equation y = 0.05 sin 50x. The amplitude here is 0.05, one-twentieth the size of the main curve. Get the period by setting 50x = 2 pi, or x = pi/25.

For every cycle of the main curve, which fluctuates between +1 and -1, you get 25 fluctuations of the other curve. Each of those fluctuations produces a small "bump" or wrinkle in the main curve, increasing or decreasing its amplitude by plus or minus 0.05.

Thus, for example, when the main curve is near y = sin (pi/2) = 1 (a maximum), the secondary curve makes it fluctuate between 1.05 and 0.95 over a very short distance.

That explains your y function.

Answer 2

You can always apply a TI-89 to this. But my gross observation is this:

y = sin x is the familiar sine wave. It goes up and then down and then up and then down like a roller coaster. sin(50x) does the same, only 50 times faster. It has 50 maxima for every 1 maxima of sin(x). But it is multiplied by the small quantity 0.05. So you get a little crinkly line around the x axis. Add this to the sine wave, and the result is a crinkly sine wave, maybe like the cross-section of a Pringles potato chip.

Answer 3

A zoomed in graph of y= sin x + .05 sin (50x)

http://www.pureai.com/Math/Graph.htm