Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

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 ) ,

(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 .

(13.32)

However, problems are often encountered when using this expression because the space ...