22 



ACOUSTICAL RADIATING SYSTEMS 



rated by a vanishingly small distance 8r. The strength of the doublet is 

 4TrJ'8r. Let J'8r = A. In these considerations A' corresponds to A of 

 equation 2.1, that is ^-kA' = S^o- 



At a distance r in a direction inclined at an angle a to the axis of the 

 doublet the velocity potential is 



<t> = 



(l+j,y 



^jk(ct-r) cos a 



The pressure from equation 2.7 is 



d(j) .pckA (\ . \ ^^, , . 



p = — p — = —J I - +jk] t^^'^"^-'"' cos a 



dt r \r / 



Retaining the real parts of equation 2.8 



pckA r 1 . , , . , , , s "I 



p = - sm k\ct — r) -\- k cos k\ct — r) cos a 



At a very large distance 



At a very small distance 



k^A 

 p oc cos a 



kA 

 p « — - cos a 



1.1 



2.8 



2.9 



2.10 



2.11 



d4> 



The particle velocity has two components, the radial — and the trans- 



1 -J J 



verse . The radial component of the particle velocity from equation 



r da 



2.7 is. 



u = 



d(f) 

 dr 



- ^~ -k 



(M)] 



A^mct-r)^Q^^ 2.12 



Retaining the real parts of equation 2.12 



u = - A 



\r^ r) 



Ik 



cos k{ct — r) sin k{ct 



-r)] 



At a very large distance 



Ak^ 



u oc COS a 



r 



cos a 2.13 



2.14 



