(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 38891, 837] NotebookOptionsPosition[ 22216, 536] NotebookOutlinePosition[ 38787, 833] CellTagsIndexPosition[ 38744, 830] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[StyleBox["Longitudinal waves through a lattice", "Subtitle"]], \ "Input", CellChangeTimes->{{3.485777145263275*^9, 3.485777182890541*^9}, { 3.4857772760695047`*^9, 3.4857772996411457`*^9}, {3.485886443662616*^9, 3.4858864448170176`*^9}, {3.4859077213270044`*^9, 3.485907746053048*^9}, { 3.485961122116884*^9, 3.4859611242540884`*^9}}], Cell[TextData[{ "The animation shows a longitudinal wave moving through a lattice of \"atoms\ \" that move to the left ", StyleBox["and", FontSlant->"Italic"], " to the right as the wave moves to the left ", StyleBox["or", FontSlant->"Italic"], " right. Clicking on the \"+\" symbol next to the slider for \"Time\" will \ reveal a \"play\" button (black triangle) as well as controls for speeding up \ and slowing down.\n\nWave number (", StyleBox["k = 2 ", FontSlant->"Italic"], "\[Pi] ", StyleBox["/ ", FontSlant->"Italic"], "\[Lambda]) and Lattice spacing (", StyleBox["a", FontSlant->"Italic"], ") are displayed along with the ratio of the lattice spacing to the \ wavelength (", StyleBox["a", FontSlant->"Italic"], " ", StyleBox["/", FontSlant->"Italic"], "\[Lambda]). It is recommended that the lattice spacing be left at the \ default value (1 nm) while the wave number is adjusted. The product of the \ wave number times the lattice spacing (", StyleBox["k a", FontSlant->"Italic"], ") gives the phase difference between adjacent atoms (this can be seen \ clearly by setting the product equal to \[Pi]). \n\nThe behavior of the \ lattice is periodic in the variable ", StyleBox[" k a", FontSlant->"Italic"], ". 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