160 



ASSOCIATED EQUIPMENT: DOMES AND BAFFLES 



calculations indicate that /8 s= 1.5.) GS The cross sec- 

 tional area of the shadow is roughly A immediately 

 behind the baffle and decreases to zero at a distance 

 approximately pA/faX.) from the baffle. But even in 

 the shadow region the sound pressure is not zero, the 

 exact pressure distribution in the shadow depending 

 upon the size, shape, and material of the baffle. Since 

 the shadow of a circular disk baffle (air or steel) has 

 been studied both theoretically and experimentally, 

 it will be used as an example. Because of the sym- 

 metry of the circular baffle, the shadow is symmetrical 

 about the axis. Thus, Figure 3, which shows the 

 shadow region in a plane containing the axis, can be 

 revolved about the axis to give a three-dimensional 

 picture of the shadow region. The interference maxi- 

 mum on the axis— the "bright" spot— is due to the spe- 

 cial symmetry of the circular baffle and would not be 

 present if the baffle were another shape, such as rec- 

 tangular. 1 ' On the other hand, the converging of the 

 outer surface of the shadow due to the increase in size 

 of an illuminated annular ring always occurs. 



In addition to the bright spot, there are alternate 

 bright and dark rings around the axis in any plane 

 parallel to the baffle. Figure 4 shows the variation of 

 pressure obtained experimentally' in the shadow of 

 18-inch and 14-inch diameter circular and 4x8 foot 

 rectangular air-filled baffles along a line through the 

 axis and parallel to the baffle diameter, at various 

 distances from the baffle with 10-, 20-, and 40-kc 

 sound. These patterns are in general agreement with 

 theoretical expectations. J 



Thus, for a baffle to be at all effective in shielding 

 a transducer with a fairly large active face, that is, an 

 echo-ranging projector, the baffle must have a large 

 transmission loss (for example, ^ 25 db), must be 

 considerably greater in area than the transducer, and 

 must be placed appreciably nearer to the latter than 

 A/(tt\). To make this statement more precise, the ef- 

 fect of interposing a baffle between a transducer and 

 a source is considered for two cases: 



h In the rectangular case, the energy previously concentrated 

 by the circular baffle into the axis bright spot would be more or 

 less uniformly distributed among several interference maxima 

 within the shadow zone. Because of the "energy redistribution" 

 the shielding effects of circular and rectangular baffles of com- 

 parable size on actual transducers (for example, the rather large 

 echo-ranging projectors) are, at the distances used in practice, 

 roughly equivalent. 



' These patterns were obtained at the Orlando test station of 

 USRL. The sound field was measured with a small size hydro- 

 phone so that the pressure at individual points in space was 

 obtained. 



BAFFLE TRANSDUCER SEPARATION IN CM 



Figure 5. Decrease in front transducer response due to 

 baffle. 



1. The transducer faces the source: front trans- 

 ducer response. 



2. The transducer faces away from the source: rear 

 transducer response. 



Case 2 is of practical interest, corresponding to the de- 

 crease in the rear response due to the baffle. Quan- 

 tities applicable to cases 1 and 2 respectively are de- 

 fined as follows: 



SR = change in front transducer response due to 



baffle interposition, 

 8R' = change in rear transducer response due to 



baffle interposition. 



J Thus, the variation of pressure p (within the shadow zone) 

 with perpendicular distance y from the baffle axis, and at a dis- 

 tance x behind a circular baffle, is 



P = P: 



i /V\- + rt 2 +v L, -v\ 



«pL 2 "a — — -). 



p . s£p. for steel baffle 

 * axis *inc 



^ p. . for air baffle 



fine I 



for y not too close to the shadow boundary (7 = zero order Bes- 

 sel function).'See reference 68, equations (23) and (24). The theo- 

 retically expected values of p . and of the positions giving the 

 edges of the blight spot are indicated on the diagram. 



