(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 2735459, 76055]*) (*NotebookOutlinePosition[ 2736380, 76086]*) (* CellTagsIndexPosition[ 2736336, 76082]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData["Longitudinal Wave Propagation"], "Title", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Times"], Cell[TextData[ "Written by Mats G. Bengtsson\nNational Defence Research Establishment\nBox \ 1165, S-581 11 Linkoping\nSweden\nemail: matben@lin.foa.se"], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Times"], Cell[TextData[ "Modified by Daniel A. Russell\nGMI Engineering & Management Institute\n\ Flint, MI 48504\nSeptember 30, 1996"], "Subsubtitle", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Times"], Cell[CellGroupData[{ Cell[TextData["Sound Waves Propagate Longitudinally"], "Subsection", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Times"], Cell[TextData[ "Longitudinal waves are conceptually different from transversal waves. \ Students can fairly easily grasp the phenomenon of transversal waves due to \ the analogy with waves on the surface of water. Longitudinal waves, however, \ are more difficult to understand, and have much wider applicability to \ physical phenomena. The propagation of sound waves is usually the first \ example to be explained with longitudinal waves. Below we try to illustrate \ how longitudinal waves propagate, but we do not try to explain why the medium \ behaves this way. The pedagocical point in this demonstration is that there \ is no transportation of atoms in the direction of wave propagation. This is a \ mere illusion."], "Text", CellMargins->{{Inherited, 81}, {Inherited, Inherited}}, Evaluatable->False, AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell[TextData["The Code"], "Subsection", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Times"], Cell[BoxData[ \(Needs["\"]\)], "Input", AspectRatioFixed->True] }, Open ]], Cell[CellGroupData[{ Cell["Longitudinal waves", "Section", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Times"], Cell[CellGroupData[{ Cell[TextData[ "Set up the configuration for longitudinal plane waves in a tube"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "Try to change the parameters and see what happens in the animation. Run the \ cells containing the code one by one, and do the animation inbetween. Do not \ mix up the two cases."], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[BoxData[{ \(\(numberOfAtoms = 1000; \)\), \(\(tubeLength = 500; \)\), \(\(tubeWidth = 2000; \)\), \(\(waveLength = 0.4\ tubeLength; \)\), \(\(waveConstant = N[\(2\ \[Pi]\)\/waveLength]; \)\), \(\(amplitude = 0.10\ waveLength; \)\), \(\(angularFrequency = N[2\ \[Pi]]; \)\), \(\(coordinatesOfAtoms = Table[{Random[Real, tubeWidth], Random[Real, tubeLength]}, { numberOfAtoms}]; \)\), \(displaceAtom[{x_, y_}] := { x + amplitude\ Sin[waveConstant\ x - angularFrequency\ t], y}\)}], "Input", AspectRatioFixed->True], Cell[BoxData[{ \(piston\ := \ Graphics[{Thickness[.01], Hue[0], Line[{{\(-20\) + amplitude*Sin[\(-angularFrequency\)\ t], \(-20\)}, {\(-20\) + amplitude*Sin[\(-angularFrequency\)\ t], tubeLength + 20}}]}\ ]\), \(tubewalls\ := \ Graphics[{Thickness[.01], Line[{{\(-50\), tubeLength + 20}, {tubeWidth + 25, tubeLength + 20}}], Line[{{\(-50\), \(-20\)}, {tubeWidth + 25, \(-20\)}}]\ }]\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell[TextData["Plot animation of plane longitudinal waves"], "Subsubsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "It is an advantage if the size of the graphics is fairly large. 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