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Phononic stop bands are formed for materials with periodic elastic properties. The material does not need to be a crystal.
The basis of phononic crystals dates back to Newton who imagined that sound waves propagated through air in the same way that an elastic wave would propagate along a lattice of point masses connected by springs with an elastic force constant E. This force constant is identical to the modulus of the material. Of course with phononic crystals of materials with differing modulus the calculations are a little more complicated than this simple model.
Based on Newton’s observation we can conclude that a key factor for acoustic band-gap engineering is impedance mismatch between periodic elements comprising the crystal and the surrounding medium. When an advancing wave-front meets a material with very high impedance it will tend to increase its phase velocity through that medium. Likewise, when the advancing wave-front meets a low impedance medium it will slow down. We can exploit this concept with periodic (and handcrafted) arrangements of impedance mismatched elements to affect acoustic waves in the crystal – essentially band-gap engineering.
The position of the band-gap in frequency space for a phononic crystal is controlled by the size and arrangement of the elements comprising the crystal. The width of the band gap is generally related to the difference in the speed of sound (due to impedance differences) through the materials that comprise the composite.
- "Sound ideas". Physics World (2005-12-01). Retrieved on 2008-01-19.
- G.P Srivastava (1990). The Physics of Phonons, CRC Press. ISBN 0852741537.