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Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition by Tim Mellow, Leo Beranek

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2.12. Cylindrical coordinates

In problems where there is axial symmetry, cylindrical coordinates are often useful, as shown in Fig. 2.16. We shall use these for planar circular radiators. In the xy plane of the rectangular coordinate system, the x and y ordinates are replaced by polar ordinates w and ϕ where the radial ordinate w is given by
w = x 2 + y 2
image (2.155)
and the azimuthal ordinate ϕ is given by
ϕ = arctan ( y / x ) .
image (2.156)
Conversely
x = w cos ϕ ,
(2.157)
y =

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