Dipoles and quadrupoles


The simplest dipole source consists of two point sources, or ‘monopoles’ of equal strength placed an infinitesimally short distance apart, operating at the same frequency but always vibrating 180o out of phase with each other. An example is given by a loudspeaker that has been removed from its box. The volume of air pushed out from the front of the loudspeaker is compensated for by the new volume of air that is pulled in from the back. This is a much less efficient way of radiating sound, as you will see if you try playing sound through a loudspeaker without a box. The animations below show that a dipole source does not radiate sound equally well in all directions. Sound is cancelled in the regions along the vertical axes.


The colour plot below shows the pressure field produced by a dipole. Red represents the positive acoustic pressure and blue negative acoustic pressure.




An observer holding and rotating a vibrating tuning fork at arm’s length from the ear will hear two loud regions in the plane of the tines separated by two quiet regions in the plane perpendicular to the fork. From the animations below, it can be seen that a similar sound field can be produced by a longitudinal quadrupole source. It is made of two dipoles lying on the same line, but oscillating in opposite phase.


When the observer holds and rotates the vibrating tuning fork close to his ear, he then finds four positions where the sound is loud, alternating with four positions where the sound is quiet. The movies below show that a lateral quadrupole source can provide a similar sound field. It is made of four monopoles with alternating phase located at the corners of a square.


Leave a Reply

Your email address will not be published. Required fields are marked *