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

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13.4. The Green's function in different coordinate systems

Rectangular coordinates

Rectangular coordinates—near-field

The Green's function in rectangular coordinates was given by Eq. (13.4) as
g ( x , y , z | x 0 , y 0 , z 0 ) = e j k R / ( 4 π R ) ,
image (13.31)
where R is the Euclidean distance, which is given by
R = ( x x 0 ) 2 + ( y y 0 ) 2 + ( z z 0 ) 2 .
image (13.32)
However, problems are often encountered when using this expression because the space ...

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