Waves unit: two experiments with standing waves

I start the waves unit with demonstrations of basic definitions.  I use a wave machine, snakey, and computer simulations to show wavelength, frequency, amplitude, transverse/longitudinal, interference, etc.  I get into standing waves pretty quickly, with conceptual demonstrations on a string vibrator.

We do two experiments:

1. We attach the 60 Hz string vibrator to a string that passes over a pulley, and which supports a hanging mass.  Varying the mass varies the wave speed; we can measure the wavelength with a meterstick.  A plot of speed vs. wavelength gives a slope of 60 Hz.

One very cool side outcome of this experiment is that it gives a visceral understanding of when standing waves can and can't form.  Students will change the wave speed, then see that the nodes and antinodes aren't happening.  They have to adjust the length of the string until the antinodes show up.  Without saying a word, I've shown my class that standing waves only occur when an integer number of half wavelengths fit into the length of the confined region.

This experiment works at any level, from conceptual physics to AP.

2. We create sound waves in an open pipe using an iphone as a variable frequency generator.  We measure the length of the pipe as a function of the frequency.  The slope of a f vs. 1/2L graph will be some multiple of the speed of sound; that multiple is the number of the harmonic.  Because we do this experiment after the one described above, many students recognize why they have to adjust the length of the pipe to get resonance; it's the same principle as when the standing wave was on a string.

It's not easy to get good data for this experiment.  I use two ~40 cm pieces of PVC that fit one inside the other, such that the total length can be adjusted continuously.  Some folks use a tub of water to provide a flexible length; that's good too, just graph f vs. 1/4L rather then 1/2L because you're using a closed pipe.

 The difficulty comes with ensuring that all the data is for the same harmonic.    I've taught my students too well to explore an entire parameter space -- they use all sorts of widely varying frequencies, and thus they jump from harmonic to harmonic, when our analysis has assumed that we control for the harmonic.  The frequency has to change very gradually, by 10 Hz or so.  When they do it right, the data looks lovely.

This experiment as described requires graph linearization, so is for honors/AP students only.  I would not do it at all with a 9th grade conceptual class -- the data collection process is two abstract, it's too difficult for 14 year olds to get good data, and plotting a recipricol requires too much calculation.

This will work for an 11th grade general class, though.  Tell the class ahead of time which range of frequencies to use.  You can arrange for everyone to use, say, the second harmonic, such that the pipe length IS the wavelength.  Then tell them to plot f vs. 1/L directly; the slope will be the speed of sound.  Because the students don't have to do the graph linearization, and because the slope is easily derived from v=λf to be the speed of sound, general-level students can handle this one.