CAVANAGH: AI^IBIENT-NOISE MODELS 



arrival angle 9p>, the transmission ratio (ratio of intensity at range 

 R to intensity at unit distance) is 



T(R,(i);eR) = S(R,9g) B(R,c});eg) . (2) 



Here 3(R/'|';9s^ accounts for boundary losses and volume attenuation 

 while S(R,6g) is the geometrical divergence factor. From the 

 reciprocity principle,* the transmission ratio is independent of 

 source/receiver identity to within a factor of sound speeds squared. 

 Hence, the .spreading loss can be written as 



COS0 



SiR.Qa) = —7-r=-^ ^-Itt^ I (3) 



W) 



smOg 



where C , C denote the speeds of sound at source and receiver. 



From (1) - (3) it follows that the differential intensity dl 

 contributed by area dA = RdRdcJ) at range R and bearing (J) via this 

 transmission path ((j)^) is 



dl(ej^,(j); dA(R,(|))) 



P(R,(t);eg)TdA 



(4) 



* In sound transmission from source to receiver as modeled with the 

 wave equation, the ratio of squared pressure to intensity at the 

 receiver (in this case, the product of intensity and sound speed) 

 remains the same when source and receiver locations are inter- 

 changed. 



811 



