Editing Wavelength (section)

==== Crystals ====
[[File:Wavelength indeterminacy.JPG|thumb|A wave on a line of atoms can be interpreted according to a variety of wavelengths.]]

Waves in crystalline solids are not continuous, because they are composed of vibrations of discrete particles arranged in a regular lattice. This produces [[aliasing]] because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure.<ref name=Putnis>See Figure 4.20 in {{cite book |author= A. Putnis |title=Introduction to mineral sciences |url=https://archive.org/details/introductiontomi00putn |url-access= registration |page=97 |isbn=0-521-42947-1 |year=1992 |publisher=Cambridge University Press}} and Figure 2.3 in {{cite book |title=Introduction to lattice dynamics |author=Martin T. Dove |url=https://books.google.com/books?id=vM50l2Vf7HgC&pg=PA22 |page=22 |isbn=0-521-39293-4 |edition=4th |year=1993 |publisher=Cambridge University Press}}</ref> Descriptions using more than one of these wavelengths are redundant; it is conventional to choose the longest wavelength that fits the phenomenon. The range of wavelengths sufficient to provide a description of all possible waves in a crystalline medium corresponds to the wave vectors confined to the [[Brillouin zone]].<ref name=Razeghi>
{{cite book
 |title=Fundamentals of solid state engineering
 |author=Manijeh Razeghi
 |pages=165 ''ff''
 |url=https://books.google.com/books?id=6x07E9PSzr8C&pg=PA165
 |isbn=0-387-28152-5
 |year=2006
 |publisher=Birkhäuser
 |edition=2nd
 }}</ref>

This indeterminacy in wavelength in solids is important in the analysis of wave phenomena such as [[energy bands]] and [[phonons|lattice vibrations]]. It is mathematically equivalent to the [[aliasing]] of a signal that is [[sampling (signal processing)|sampled]] at discrete intervals.