9887

Acoustic Multipoles

Acoustic waves are produced by successive phases of volume expansion and contraction. In contrast to electromagnetic waves, their polarization is longitudinal. Depending on the number of sources and their geometry, different patterns can be created. The simplest case, with spherical symmetry, is the monopole (e.g. from a boxed loudspeaker). Other common cases are the dipole (from an unboxed loudspeaker) and the lateral quadrupole with four monopoles, with the two pairs out of phase with one other.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The solutions can be derived from the acoustic wave equation
,
where is the acoustic pressure and is the speed of sound.
The simplest acoustic source is the monopole,
.
Taking the spatial derivative of the last expression, for the case of a dipole, we find
,
and taking the second spatial derivative, for the quadrupole, gives
.
References
[1] D. A. Russell. "Acoustics and Vibration Animations." (Sep 27, 2013) www.acs.psu.edu/drussell/Demos/rad2/mdq.html.
[2] D. A. Russell, J. P. Titlow, and Y. Bemmen, "Acoustic Monopoles, Dipoles, and Quadrupoles: An Experiment Revisited," American Journal of Physics, 67(8), 1999 pp. 660–664. doi:10.1119/1.19349.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+