154 



ASSOCIATED EQUIPMENT: DOMES AND BAFFLES 



in the pattern, increasing such effects as the rear re- 

 sponse. However, if the domes are well designed 

 acoustically, these additional side lobes are usually 

 over 20 db down with respect to the main lobe. For 

 this reason it is generally desirable to distribute the 

 sonic energy contained in a single internal specular 

 reflection among many directions unless the specu- 

 larly reflected beam can be intercepted and further 

 subdivided or absorbed. 4 *-"' 1 ' Furthermore, the enclo- 

 sure of a transducer in a dome should not appreciably 

 alter the width of the main lobe or increase the mag- 

 nitude of the side lobes already present in the trans- 

 ducer patterns. (These two effects are quite small in 

 well-designed domes.) 



Third, the enclosure of a transducer in a dome 

 should not appreciably alter the radiation impedance 

 of the transducer. (Impedance change is usually very 

 small in well-designed domes.) 



Acoustical disturbances introduced by domes, such 

 as specular reflections and transmission losses, are in- 

 terrelated. In general, a dome which introduces small 

 transmission losses also causes small specular reflec- 

 tions. (A quantitative relation between the two is 

 given later.) Moreover, because the change in the 

 radiation impedance of the transducer is small, its 

 total power output is unaffected by enclosing it with- 

 in a dome; also, true absorption of sound within the 

 dome wall is negligible for metal domes. As a result, 

 the energy which is removed by the dome wall from 

 the impinging transducer beam and which consti- 

 tutes the transmission loss is redistributed in direc- 

 tions other than the original direction of incidence; 

 in particular, the major portion of this energy is con- 

 centrated into the direction of specular reflection." 

 This redistribution has the effect of increasing the 

 value of the directivity factor 8. (The directivity fac- 

 tor is related to the directivity index by the expression 

 A = 10 logg. See Chapters 3 and 4.) Thus, for an 

 echo-ranging projector: 114 



p = bll = / j '' 28 ' (i) 



Pci'ii Po c o 



where 



P = acoustic power output of echo-ranging pro- 

 jector, 

 /;, = axis pressure output of bare projector at 1 

 meter, 



pi = axis pressure output of dome-enclosed projec- 

 tor at 1 meter, 



8 = directivity factor of bare projector, 



8' = directivity factor of dome-enclosed projector, 



p„ = density of water, and 



r n = velocity of sound in water. 



Therefore, the one-way transmission loss TL intro- 

 duced by the dome, defined by 



a Thus, the magnitude of ihe additional side lobes introduced 

 by the dome into the directivity pattern, for example, the addi- 

 tional rear response, increases as the transmission loss increases. 



TL = 201ogfl 7) 

 Pi 



is, from equations (1) and (2) 



IT. -20 log |\ 



(2) 



(3) 



Thus, the expression TL is a measure of the change 

 in the transducer directivity index introduced by the 

 dome. 



Expressions may now be obtained theoretically for 

 the magnitudes of both the transmission loss and the 

 specular reflection induced by a dome of given mate- 

 rial, wall thickness, and dimensions, on an enclosed 

 transducer of given frequency, directivity, and posi- 

 tion within the dome. 48 These expressions are found 

 by determining the effect of dome enclosure on the 

 sound field of a transducer; they agree generally with 

 experimental tests on domes performed by USRL. b 

 The expression for the transmission loss (and so by 

 equation (3) for the dome-induced change in direc- 

 tivity index) is: 



TL = 10 log 



1 + 



mn 



(4) 



where 



Pi = density of dome wall material, 



Pn = density of water, 



(/ = thickness of dome wall, 

 , 2,r _ 2»/ 



" = A V 



Ao '(i 



A,„ < ,, = wave length and sound velocity in water, 



and 



/ = frequency. 



hSee SIR Division fi, Volume 11. 



