Acoustic Bipole and Tripole

An acoustic bipole consists of two identical monopoles driven in phase (whereas, in a dipole, they are out of phase), separated by a short distance along the axis. As shown in the Details section, the radiated sound produces a directivity pattern , where is measured between the point of observation and the normal of the bipole and stands for the wavenumber.

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DETAILS

The radiation field for a bipole is
,
where the directivity pattern can be written as
.
For the tripole
and
See Part 6 of [1].
Reference
[1] P. B. Nagy. "Acoustic Radiators." (Nov 9, 2001) www.ase.uc.edu/~pnagy/ClassNotes/AEEM7028 Ultrasonic NDE/.

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