362 



THEORY 



ject. Equation (56) is the so-called Rayleigh scatter- 

 ing law. The echo intensity is directly proportional 

 to the square of the volume of the target and in- 

 versely proportional to the fourth power of the wave- 

 length; thus, the echo intensity drops off rapidly as 

 the wavelength increases. 



20.7 



EFFECT OF PULSE LENGTH 



All the previous discussion in this chapter has been 

 concerned with sound waves emitted in an essentially 

 continuous fashion. While Section 2.3 discussed the 

 effect of pulse length in terms of ray acoustics, this 

 section will describe the effect of pulse length on the 

 observed target strength in terms of wave acoustics, 

 developed from the analysis in the preceding sections 

 of this chapter. 



It was .shown in Section 12.2 that at any instant 

 the scattered sound energy received back at the 

 transducer from the projected pulse comes from a 

 spherical shell of thickness cr/2, where c is the sound 

 velocity and r is the duration of the pulse. This result 

 is still true on the more accurate wave theory pre- 

 sented in Section 20.2, as long as the fluid is homo- 



geneous and the target is rigid and convex. From a 

 concave target, sound reflected several times may 

 arrive later than singly reflected sound. 



This thickness ct/2 is known as the pulse length. 

 When the pulse length is so long that it includes many 

 Fresnel zones, the echo level will be essentially the 

 same as that observed for continuous soimd, pro- 

 vided the echo is measured at a time when the wave- 

 lets are arriving from all these zones. At the beginning 

 of the echo, when only the first few zones are con- 

 tributing, and toward the end, when only the last 

 zones return wavelets to the source, the echo struc- 

 ture is more complicated. However, an application of 

 the Fresnel zone theory would probably give correct 

 results in this case. 



When the pulse is only a few Fresnel zones long, 

 the echo structure is presumably more complicated, 

 and the echo duration, for example, may be expected 

 to exceed the duration of the outgoing pulse. The 

 pulse length cannot be less than the thickness of a 

 Fresnel zone, since in that case the outgoing pulse 

 would consist of less than half a cycle, and the wave- 

 length would cease to have much meaning. 



