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APPARATUS

The crystal model is a periodic array of alternating pieces of pvc pipe and plastic irises.  There is a speaker at one end and a computer-interfaced microphone at the other.  The computer sound card and software is used to sweep through a range of frequencies and plot the transmission spectrum.  The sound waves in the tube are partially reflected at the irises.  When the array spacing is equal to an integer multiple of one-half wavelength, the reflected waves interfere constructively and little sound is transmitted to the microphone, so gaps appear in the transmission spectrum.  This is analogous to interference of the electron wavefunction in a crystal lattice.

The length of a unit cell, a, is 17.9 cm.  The frequency spectrum shows band gaps centered around integer multiples of f = v/λ = v/2a = 958 Hz.

Set up the software to sweep from 0 to 12,000 Hz or whatever range you like in 10 Hz steps, with the time per step set to 50 ms and the FFT filter on.

The spectrum below was made using seven cells of 17.2 cm pvc pieces separated by the larger diameter irises.

This array is 1.25 m long.  For comparison, you can remove the irises, add the short pvc spacer to compensate, and show the resonances of a tube of this length alone.

A longer section representing a crystal defect can be inserted in the middle, to introduce an allowed state within the band gap.

The program is spectrumSLC.exe.

The microphone should not touch the wall of the tube.

JASA 112, 1353 (2002)

AJP 50, 1137 (1982)

AJP 72, 255 (2004).

AJP 70, 689 (2002).