In conceptual physics, I want to do an experiment with a 60 Hz frequency generator and waves on a string. The setup is shown in the picture to the right: the hanging mass is varied, varying the tension in the string and thus the wave speed and the wavelength. We move the generator left and right until the standing waves are clear; then we measure the wavelength with a ruler.

I want to plot wave speed vs. wavelength, so that the slope of the straight-line graph will be the 60 Hz frequency.

Problem is, I don't have an instrument to measure wave speed on the string. In AP physics, I'd just show the students the equation

and let them figure out the wave speed for themselves.

Well, this is 9th grade conceptual physics. Most of my students either have not completed algebra 1; most wouldn't know a square root if it bit them on the arse.* I can not expect my class to be able to plug into this formula. But I still need them to be able to graph a wave speed, knowing only the mass of the hanging mass.

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*That happened to me once.*

One thought I had was to create a quick app to make the calculation: On an iphone or ipad, it could ask "What's the hanging mass?" Then, using the linear mass density value I measured for the string before class, I could program the app* to spit out "the wave speed is 3000 cm/s." Yes, I know I could do something like this in excel or on wolfram alpha, perhaps, but anything beyond a mass input in grams followed by a speed output in cm/s is too complicated for me.

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*That is, if I knew how to program ios apps. Hey, now, if I had access to a 1985 version of applesoft basic, I'd pwn all of ya in a programming contest. And I'd have that "app" ready in five minutes.*
Without the ability to make the program I want, I realized that I could go all 1940s and just create a lookup table. Excel will do the calculation... in fact, I learned how to get excel to round the speeds to two significant figures. So I put mass values from 5 g to 300 g in one column. I made excel use the equation above to calculate the wave speed in units of cm/s.

Then I just printed the two columns. I'll hand this out to each lab group. I think it's totally reasonable to expect freshmen to use this table to relate the hanging mass to the wave speed... then to graph wave speed on the vertical, and the measured wavelength on the horizontal.

GCJ

Wouldn't it make more sense to turn this around. They can measure the mass and the wavelength, and be told that the frequency generator is 60Hz. Then have them plot the wave speed as a function of tension?

ReplyDeleteI started having students write programs on their TI graphing calculators to solve for variables, like so! http://education.ti.com/calculators/tiphysics/US/Activities/Detail?id=13656

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