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

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15.5. Effect of discretization into rings of finite width

Rings of Equal Delay. One option might be to vary the widths of the rings so that there are equal delay sections between them, in which case the on-axis pressure is
p norm = k a D ( 0 ) = k a n = 0 N e j k a n + 1 / 2 N + 1 ( a n 2 a n 1 2 a 2 )
image (15.21)
where the radius of the nth ring is
a n = a 1 ( 1 n + 1 N + 1 ) 2 ,
image (15.22)
a 0 is the radius of the center disk and a 1   =  

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