CAUTION: This apparatus is not meant to operate at very low frequencies. When setting the frequency range of your scan, do not start below 500 Hz. Even then you may see some low-frequency noise that is not worth analyzing.

DON’T RUSH! Take your time and think about how/why your data has changed after you’ve changed the apparatus.

4.1 Making Connections and Measuring the Speed of Sound

1. Start with a 400 mm column (8×50 mm tubes).
2. Start by getting your sound wave ready.  Turn on the function generator.  Set the frequency to 500 Hz and the amplitude to 350 mV.  Plug the function generator output into the ‘sine wave input’ on the electronics box.  Plug the output of the frequency-to-voltage converter into channel 1 of the oscilloscope.
3. Plug the microphone into the ‘microphone input’ on the electronics box.  Plug the ‘AC monitor’ in to channel 2 of the oscilloscope.
4. Use the ‘display’ menu to switch to XY mode.  Now the voltage-that-represents-frequency is on the x-axis and microphone channel on the y-axis.  Adjust the position on the scope and DC offset on the electronics box such that the locus of points is near the bottom left corner of the screen.  Still in the ‘display’ menu, set the ‘persist’ to infinity.
5. Now start sweeping the frequency in the 10 Hz decade (i.e. change the frequency by 10 Hz with every click of the rotary knob).  The signal on the scope should start sweeping to the right and drastically increasing in amplitude when the resonance condition is met.  You can stop once your at like 7 or 10 kHz
6. Now that we know things are working, we can start taking measurements.  You have two options:  You can stay in XY mode and zoom in the x-axis so that you can very clearly see what frequency generates the largest amplitude.  Or you can switch to YT mode and look at the amplitude of the signal from the microphone and adjust the frequency to maximize it.  Either way, you’ll likely need to turn off the persist.
7. Start from the high frequency you ended your scan at.  Record enough resonant frequencies that you could trust the results of a linear least squares fit.

4.2 Lattice Simulations

1. Now introduce lattice sites by placing a 16-mm inner-diameter iris after each piece of tube. Do another long-range frequency scan so you can see the Brillouin zones and band gaps.  Record the frequency ranges of the band gaps and Brillouin zones.
2. Do more precise scans over the Brillouin zones and record the frequency of the k-points in each zone.
3. Remove a unit cell (tube+iris) and repeat the frequency scan, recording the size of the band gaps, Brillouin zones, and frequencies of the k-points. Then remove another unit cell and repeat.  You should notice a pattern forming. HINT: Count the resonances in the Brillouin zones.
4. Go back to using eight 50-mm tubes and 16-mm iris’s and take an initial data set. Now vary the length of the tubes and do frequency scans. Again, be on the lookout for patterns that develop.
5. Go back to using eight 50-mm tubes and 16-mm iris’s and take an initial data set. Now vary the iris diameter and do frequency scans. As always, be on the lookout for patterns that develop.