348 



PRINCIPLES 



Figure 3. Uniform reflection from a sphere. 



range. At long ranges, then, only the transmission 

 loss term depends on the range. 



At short ranges, however, the target strength de- 

 pends on the range as well as on the size, shape, and 

 orientation of the target (see Section 20.4.4). If the 

 source is so close to the target that different parts of 

 the target are struck by sound of different intensities, 

 or if the receiver is so close that the spreading of the 

 sound reflected from the target to it is not the same 

 as the spreading from a point source, the target 

 strength term will depend on range. Therefore, at 

 short ranges equation (6) does not serve primarily to 

 separate the effects of range, transmission conditions, 

 source level, and target characteristics on the echo 

 level, but rather to define target strength under the 

 particular conditions of that measurement. 



19.2 TARGET STRENGTH OF A SPHERE 



Because a sphere is perfectly symmetrical, the 

 echoes which it returns to a sound source are com- 



pletely independent of its own orientation. For this 

 reason, spheres are convenient targets and have fre- 

 quently served as experimental targets in echo-rang- 

 ing measurements. In this section, the target strength 

 of a sphere will first be derived simply and intuitively 

 by considering the total intercepted and reflected 

 energy without regard to the angular distribution of 

 energy within the reflected sound beam. Then a more 

 rigorous derivation — within the framework of ray 

 acoustics — will be presented, in which the angular 

 distribution of the reflected energy is considered in 

 detail. 



19.2.1 



Simple Derivation 



Consider a plane wave of sound of intensity /o 

 striking a sphere of radius A and cross-sectional area 

 tA^. Then the total sound energy intercepted by the 

 sphere per unit time will be ttA^Iq and, if reflection is 

 perfect, the total sound reflected from the sphere per 

 unit time will also be irA^Io. 



