Mechanics > Properties of Matter > Crystal Structure DCS# 1R50.xx

ACOUSTIC 1-D CRYSTAL ANALOG




APPARATUS
pvc acoustic crystal model
209-02-C6
aluminum channel support piece
209-02-D
speaker with pvc coupler
209-02-C6
microphone
202-07-E3
amplifier
202-09-B
laptop
206

DESCRIPTION
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.
NOTES
The program is spectrumSLC.exe.

The microphone should not touch the wall of the tube.

REFERENCES
JASA 112, 1353 (2002)

AJP 50, 1137 (1982)
AJP 72, 255 (2004).

AJP 70, 689 (2002).