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Teaching Room Modes and Diffraction Using Comsol
Multiphysics
Ralph T Muehleisen Formerly of
Ill. Inst. of Technology
Soon to be Principal Building Engineer
Argonne National Lab
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This presentation will show the use of a finite element software
for teaching room modes and diffraction
Diffraction
Room Modes
Demo
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Why Comsol Multiphysics? There are lots of good free and pay FEM
software packages. I use Comsol Multiphysics because: Its a General
Purpose Non-Linear Coupled PDE solver using
Finite Elements that links to MATLAB Evolved from the MATLAB PDE
solver If you can write a PDE for it, it can probably solve it
Has add on Prepackaged Analysis Modes (like Matlab toolboxes)
that set up the equations and analysis modes for you for easier use
The program lets you modify/augment the preset modes to
investigate
coupled physics EDU pricing is really pretty darn good.
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Diffraction can be difficult concept to explain
Math can be quite hard We cannot see sound
so seeing diffraction is hard
Demos/experiments like ripple tanks work well but require space
and maintenance and are not portable
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Computational software lets you visualize acoustic
diffraction
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Diffraction around barrier where h=4 (this is high freq where
the barrier is effective)
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Diffraction around barrier where h=4 (this is high freq where
the barrier is effective)
Interference patterns from reflected sound are clear
High attenuation of sound in shadow zone
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Diffraction around barrier where h= (this is low freq where the
barrier is less effective)
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Diffraction around barrier where h= (this is low freq where the
barrier is less effective)
Interference patterns from reflected sound are less clear
Low attenuation of sound in shadow zone
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Resonant modes are conceptually easy, except they are not .
Most texts and teachers start explaining standing waves and
modes as a superposition of waves traveling in opposite
direction.
In rectangular rooms the mode shapes naturally drop out of the
math
( )( )( , )2 cos( )cos( )
y yx x jk y jk yjk x jk x j t
j tx y
p x y A e e e e e
A k x k y e
= + +
=
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Resonant modes are conceptually easy, except they are not .
Most texts and teachers start explaining standing waves and
modes as a superposition of waves traveling in opposite
direction.
In rectangular rooms the mode shapes naturally drop out of the
math
( )( )( , )2 cos( )cos( )
y yx x jk y jk yjk x jk x j t
j tx y
p x y A e e e e e
A k x k y e
= + +
=
Superposition of plane waves
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The Problem With This Analysis
The problem with that analysis is students then naturally assume
that if you slant the walls of the room, youll keep the plane waves
from reflecting in phase and eliminate room modes
It is much harder to explain the concept of eigenfunctions of
boundary value problems and even harder to convince students that
all rooms have mode shapes when analytic solutions do not exist
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The Answer
FEM software lets you compute and show students that other
shapes have modes too
Start with a rectangular room and show resonances Splay one wall
and show the resonances Splay two walls and show resonances Splay
all walls and show resonances Draw an amorphous shape room and
compute the
resonances in class.
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1st 3 Modes of Several Similar Rooms
Rectangular 1 Splay Wall 2 Splay Walls Amorphous
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Questions?
In summary, FEM software like COMSOL can be very useful to
visualize some complex acoustic phenomena
You can show diffractive bending of waves around objects
You can show that all rooms, of any shape, have modes
Teaching Room Modes and Diffraction Using Comsol
MultiphysicsThis presentation will show the use of a finite element
software for teaching room modes and diffractionWhy Comsol
Multiphysics?Diffraction can be difficult concept to
explainComputational software lets you visualize acoustic
diffractionDiffraction around barrier where h=4 (this is high freq
where the barrier is effective)Diffraction around barrier where h=4
(this is high freq where the barrier is effective)Diffraction
around barrier where h= (this is low freq where the barrier is less
effective)Diffraction around barrier where h= (this is low freq
where the barrier is less effective)Resonant modes are conceptually
easy, except they are not .Resonant modes are conceptually easy,
except they are not .The Problem With This AnalysisThe Answer 1st 3
Modes of Several Similar RoomsIn summary, FEM software like COMSOL
can be very useful to visualize some complex acoustic phenomena
