MaplePrimes - answers and comments on Question, Plotting standing waves

Ambiguity

rlopez — Thu, 15 Dec 2011 01:16:31 Z

The question asks for help graphing standing waves. Then it goes on to "clarify" by stating "what would happen if different types of waves traveling..."

Well, you either want to graph standing waves, in which case nothing moves, or you want to graph traveling waves where you can see two waves interacting. And for this, you need to add two waves, not multiply them. For the traveling waves, you also have to decide if they are traveling on an infinite line, or are they reflecting off a fixed endpoint.

RJL Maplesoft

Animation with sliders

rlopez — Mon, 19 Dec 2011 21:02:25 Z

The interactiveparams command in the plots package will generate an animation on one parameter with control of other parameters by sliders. For example, to animate the graph of x+a+b, with a being the animation parameter and b being under the control of a slider, use

interactiveparams(animate,[plot,[x+a+b,x=0..1],a=0..1],b=0..1);

One way to discover this syntax is to launch the Plot Builder on the expression x+a+b, and to select Interactive Animation with 1 parameter in the "Select Plot Type anbd Functions" section. Then, check the box at the bottom, to the right of "On 'Plot" return command". The syntax for the appropriate use of the interactiveparams command will be returned. Of course, if this box isn't checked, the Plot Builder itself will generate the graph with the sliders. The one disadvantage of the interactiveparams command is that it launches a Maplet, which can't be saved or embedded in the worksheet. It's ephemeral, living only as long as it's "up."

The alternative is to use the animate command, and simply change the value(s) of the parameter(s) in each different animation.

RJL Maplesoft

Standing waves

Robert Israel — Thu, 15 Dec 2011 02:25:18 Z

Robert: I think what seanstnn means is this. A standing wave can be created by the interference of two waves of the same amplitude moving in opposite directions:

> expand(cos(omega*(x-k*t)) + cos(omega*(x+k*t)));

You might try something like this:

> plots:-animate(plot,[cos(x-t)+cos(x+t),x=0..4*Pi],t=0..2*Pi);

Thanks Robert, I'm trying to vary omega and k to see if I can get some other effects.

seanstnn — Sun, 18 Dec 2011 20:56:22 Z

Do you know a convenient way to do this in the animation function/context? I am actually trying to make a pair of opposing waves that converge into a spiral. I have seen a parametric equation pair that does just this but can no longer find it. The result is what looks like a modulated signal that moves from the second quadrant into the first quadrant and then begins to spin around in a spiral. It's more complicated than simple standing waves...I think it has a cos() with a decaying exponent exp() piece that begins to dominate the sinusoid in the first quadrant and causes the modulated signal to collapse in a spiral....I think you can make a torque on the end of a standing wave. That's what I'm investigating.