# 1D Mechanical Waves

Once again, I would like to say that for those that have never attended a modeling workshop, although I hope this series of blogs peaks your interest, in no way should they be viewed as a replacement. Compared to the first set of workshop, I will not be posting links to the materials used as ASU and the AMTA have chosen to keep them under lock and key. If you are offended by that, I’m sorry, but they have chosen to restrict some materials, and I am in no place to challenge them. The basic thought process is that there research has shown that one best learns through doing, not through being told.  Therefore, the best way to learn how to implement modeling is to experience modeling for yourself, not to read about it.  In short, if you just read how to model, try to use it and find it ineffective, it could very well be you implemented it incorrectly.  Go to the workshop, you’ll thank me.  For those readers that have attended the Mechanics workshop, this may help you sort through the materials to which you have access, but again, you might want to try to get to one of these if you can.

As we ended the particle model unit, we had a good discussion about the overall storyline of this collection of units.  I think I’ll let this play out a little more, but I can’t help but think that this storyline is making it more difficult than it needs to be.  For those that don’t know, there is modeling material for just mechanical waves.  I haven’t had a chance to really go through them, but there are units for the oscillating particle model, 1D wave model, sound, and then 2D waves.  To me, that would flow very nicely out of the central force particle model.  With that in mind, I’m thinking you could just go straight into the wave model of light.

I’m fully aware that the current progression of starting with the particle model of light is true to an historical approach, but the major aspects of reflection and refraction could just as easily be first introduced with a wave model.  As you then move in to the photoelectric effect and the beginnings of the Bohr Model, you could then bring in the particle nature of light (yes, the photon model is distinct from a particle model, but what is the end product the kids NEED to know.)

Anyway, just some food for thought.  From what I can tell, this collection of three units is set up to be taught without teaching the mechanical wave units, thus this post will look at introducing mechanical waves to students.  To me, if you do include those units, you can skip this content and move directly into building the wave model for the behavior of light.

We begin this unit by asking the question, “What would you have to do to make a wave?”  You then provide some Super Slinkies or “Snakies” (or both) and have the kids go play.  By time they are done, your should be able to discuss the characteristic variable (frequency “$f$,” wavelength “$\lambda$,” speed “$v$,” and amplitude “$A$“), what you need to do to increase the speed (effects of tension, amplitude, and distance on wave speed), and how non-conservative energy loss (due to friction) effects wave propagation.  If you want, you can pose these as questions to answer, or just let them play (and if need to send them back out to play a second time).  How much guidance would depend on the maturity of your kids.  One other important concept that you need to get across is that with waves, energy moves, even though there is not net displacement of the medium.

By connecting the Slinky to the Snaky, you can also begin to show that the speed of the wave depends on the medium.  If the students are really careful, by sending two quick pulses, they can feel that the frequency is independent of the medium.

The second major activity/lab is to get the students to see that the speed of the wave is a product of frequency and wavelength.  The modeling materials say to do this through the introduction of standing waves. To me, that might be too big of a jump.  Instead, I think you could have the kids measure the speed of a pulse  by measuring distance and time (possibly include various tensions) first, then bring in standing waves (and find frequency times wavelength) and compare to speeds found already.  Another option would be to video tape the waves and use video analysis to determine the speed of the wave.  In the end, with standing waves you need to build in the terms node and antinode.

During the standing wave lab, we had “major” issues trying to measure the variables using the snaky.  We later saw that the teacher notes say to use a slinky since it has less tension.  The other option is to use a wave generator which can better oscillate at a controlled rate.

At some point during this process you need to talk about reflection, interference, and superposition.  Student should see that both the wave model and the particle model can account for reflection (As you get to 2D waves, you can further show the behaviors of reflection discussed in the particle model).

From there, we completed worksheet #1 and later whiteboarded our results. If the kids didn’t notice it already, you can discuss transverse and longitudinal waves, along with terms such as crest, trough, compression, and rarefaction.

As mentioned at beginning, to me, this could just as easily be its own unit (most likely leading into another unit on 2D waves in water.

{The Wave Model, brought to you by FIU, CHEPRO and the National Science Foundation}