BAFFLES 



157 



The effectiveness of a baffle depends largely upon 

 its material, its size and thickness relative to the sound 

 wave length, and its location with respect to the trans- 

 ducer. When the problem of sound propagation past 

 a baffle is considered, it is found that, for a plane wave 

 incident on one side of the baffle, the pressure on the 

 other side is due to both a transmitted wave and a dif- 

 fracted wave. A sound shadow is formed behind the 

 baffle only if the transmitted wave is small. The deci- 

 bel ratio of the incident intensity to the transmitted 

 intensity (through an infinite plane baffle) is called 

 the transmission loss TLs and is given by Rayleigh's 

 formula. 78 



TL = 10 log f 1 + i (B&- ^Y s.n^l (6) 



where 



TL = transmission loss, 

 p = density of water, 

 c = sound velocity in water, 

 p, = baffle density, 



r, = sound velocity in baffle material, 

 d = baffle thickness (or average thickness), and 

 A t = sound wave length in baffle material. 



This expression for TL versus d/Ai is plotted in Fig- 

 ure 2 for a plane parallel baffle of air (scale 1) and 

 steel (scale 2) in water. It can be seen that a plate with 

 a large loss at one frequency will also have a large loss 

 over an extensive range of frequencies. The baffle 

 thickness is not critical as long as it is not ecpial to a 

 value appropriate to resonance transmission, that is, 

 when 2(7/A 1 is not equal to an integer. It is, therefore, 

 not difficult to obtain a baffle with a large transmis- 

 sion loss; for example, a steel plate about 1 inch thick 

 has a transmission loss of roughly 20 db at 24 kc. 

 Thus, as far as transmission loss is concerned, such 

 steel baffles are adequate; baffles containing air pock- 

 ets are generally even more effective, the loss of a 

 0.2-inch thick air baffle at 24 kc being approximately 

 60 db. 



Even when transmission loss is large, the infinitely 

 long shadow of geometrical acoustics in which the 



^f :fc: ::: 



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IfiM BAFFLE] 

 (STEEL 6*FTL£| 



Ficure 2. Transmission loss of baffles. 



sound intensity is zero is never formed behind the 

 baffle. For incident plane waves of wave length \ in 

 water, diffraction around the baffle edge limits the 

 shadow to a length of approximately fiA /(irX), where 

 A is the area of the baffle projected on the wave front 

 and /3 is a numerical factor = 1. (For a circular baffle 



PLANE WAVE 

 INCIDENT SOUND 



STEEL BAFFLE 



BAFFLE 



AIR BAFFLE 



PLANE WAVE 

 INCIDENT SOUND 



e Equation (6) reduces to equation (4) if 2-jr<i/\ 1 « 1 and 

 Pi c l/Po r o * '• conditions always satisfied by the thickness and 

 material of dome walls in current use. 



INTENSITY OF SHADING REPRESENTS SOUND SHADOW 

 (ie HEAVY SHADING CORRESPONDS TO LOW SOUND PRESSURE ) 



Figure 3. Sound pressure distribution behind baffle. 



