Analyze the Acoustic Eigenmodes of a Car: New in Wolfram Language 11

Analyze the Acoustic Eigenmodes of a Car

Compute the acoustic eigenvalues and eigenfunctions for an approximation of a cross section through a Mini.

Import an image of the cross section.

In[1]:=

img = Import[
  "http://upload.wikimedia.org/wikipedia/commons/d/d3/Mini_cross_\
section.jpg"]

Out[1]=

Use the mask tool to create a boundary graphic.

In[2]:=

boundary = \!\(\*
GraphicsBox[
{GrayLevel[1.], 
{AbsoluteThickness[1], LineBox[CompressedData["
1:eJxdkmtI0wEUxZdKWCaazxQlHyQLRckXQmQH+2sWCs5HivlhSYaKjxbF8rU0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"]]}},
Background->GrayLevel[0.],
ContentSelectable->True,
ImagePadding->{{0., 0.}, {0., 0.}},
ImageSize->{273.3999999999956, 170.4},
PlotRange->{{0, 3910.}, {0, 2535.}},
PlotRangePadding->Automatic]\);

Discretize the graphic.

In[3]:=

bdr = BoundaryDiscretizeGraphics[boundary]

Out[3]=

Compute six eigenvalues and eigenfunctions of the cross section.

In[4]:=

{vals, funs} = 
  NDEigensystem[{-Laplacian[u[x, y], {x, y}]}, 
   u[x, y], {x, y} \[Element] bdr, 6];

Inspect the eigenvalues.

In[5]:=

vals

Out[5]=

Visualize the second eigenfunction in the cross section of the car.

show complete Wolfram Language input

In[6]:=

Show[img, 
 ContourPlot[funs[[2]], {x, y} \[Element] bdr, Axes -> None, 
  Frame -> None, AspectRatio -> Automatic, 
  ColorFunction -> 
   Function[f, {Opacity[0.75], ColorData["TemperatureMap"][f]}]], 
 ImageSize -> Automatic]

Out[6]=