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meaning of monopole, dipole, quadrupole

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Old   February 26, 2008, 23:31
Default meaning of monopole, dipole, quadrupole
  #1
shh
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I'm just starting on aeroacoustics, can someone suggest some reference to read on monopole, dipole, quadrupole? A brief description here about the differences in these poles would be helpful as well.
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Old   February 27, 2008, 13:06
Default Re: meaning of monopole, dipole, quadrupole
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Jonas Holdeman
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This can be related to electromagnetics. The electric potential of a single charged particle decreases with distance from the charge as 1/r (and the electric field as 1/r^2). If there are two equal and opposite charges nearby, there are two poles or a DIpole. The fields don't exactly cancel, but the combined fields fall off more slowly, the potential like 1/r^2. If there are four charges properly arranged (so their dipole fields cancel) with net zero charge (so their monoploe fields cancel), this is called a quadrupole and the field falls off like 1/r^3. A general distribution of charge can be expanded in a series of inverse powers of r called a multipole expansion.

The mathematics generalizes to distributed sound sources. The sound intensity at some distance from the source can be represented as a multipole expansion, an expansion in inverse powers of r, the first term being the monopole, the second the dipole, etc.
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Old   February 27, 2008, 22:54
Default Re: meaning of monopole, dipole, quadrupole
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shh
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Thank you! Is there a reference book also, on aeroacoustics? I read in Hucho's Aerodynamics of Road Vehicles that quadrupole sources are not as important as dipole (pg. 345, 4th ed). In commercial CFD or CAA codes that you are used to, are all poles detected. If not, which poles are detected?
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Old   February 28, 2008, 04:25
Default Re: meaning of monopole, dipole, quadrupole
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andy
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> In commercial CFD or CAA codes that you are used to, are all poles
: detected. If not, which poles are detected?

A useful book to read on basic aeroacoustics is "Sound and Sources of Sound" by Dowling and Ffowcs-Williams. It is classical acoustics rather than computational acoustics but is pitched at final year undergraduate/first year postgraduate level.

Monopoles, dipoles, quadrupoles are models of sound sources. If you solve the Navier-Stokes equations then you have no need for these models. However, if you solve approximate forms of the Navier-Stokes equations then you may have to add back models for the acoustics that have been removed by the modelling assumptions. How to do this effectively varies strongly with the type of flow and the information one wants to know about the acoustics.

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Old   February 28, 2008, 12:53
Default Re: meaning of monopole, dipole, quadrupole
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Steve
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I like "Theoretical Acoustivs" by Norse and Ingard. ISBN 0-691-02401-4

A monumental epic!
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