ELIMINATION OF REFLECTIONS 



41 



may reduce the magnitude of the response variation. 

 An air-water interlace has a reflection coefficient close 

 to unity, but a muddy or sandy bottom may have a 

 considerably smaller one. It is evident that R may 

 also include any other factor which makes the re- 

 flected wave have a smaller amplitude, such as direc- 

 tionality of the source or of the receiver. 



It may also be noted that the frequency spacing 

 A/ between successive maxima or minima is given by 



L is the difference in path Length ol 



(6) 



where AL is the difference in path length ot the 

 direct and reflected waves, its value in the above case 



being (\/d- + Ah- - d) ■ 



The partial elimination of reflection interference 

 in test results can be accomplished by (1) reducing 

 the effective value of R by the use of directional 

 sources, screens, etc., (2) averaging out the interfer- 

 ence effects through the use of warbled frequency or 

 other multi-frequency signals, (3) making use of 

 pulses which are measured before reflected pulses 

 reach the point of observation, and (4) mathemat- 

 ically eliminating the effects of reflection from the 

 results. Each of these methods has some advantages 

 and some disadvantages which are discussed in de- 

 tail in the sections following. 



.1 .2 .3 .4 .5 .6 .7 .8 .9 1 2 J 4 J 



FREQUENCY IN KILOCYCLES PER SECOND 



Figure 2- Effect ot testing distance on response of 3A-32 

 pressure hydrophone measured with 1 J-t projector. Test- 

 ing depth = 9 ft. Water depth = II It. Testing distance- 

 as shown on curves. 



I(d,)/I„ where 0,. is the angle indicated in Figure 3. 

 Now r is given by 



d, = tan- 1 



2// 



so that 



R"-Z(tan-i^.)/ . 



(7) 



(8) 



5.3.2 



Directional Sources 



For a dipole source with axis along the line joining 

 source and receiver 



cos 2 0, 



(9) 



The simplest and one of the most effective methods 

 of eliminating any significant reflections in calibra- /(#) 



tion tests is by the use of directional sources. These I u 



must be so designed and oriented that very little 



acoustic energy reaches the surface or bottom in the S o that (using subscripts to indicate the type of 

 direction in which direct specular reflection from source), 

 the surface or bottom to the position of the receiver 

 occurs. Sources with various types of directivity pat- » 



terns may be employed, but, for practical considera- 

 tions, only three require attention: the dipole source, <7- 

 the circular piston source, and the line source. d 2 + Ah- 



If the reflecting surface is assumed to be a perfect 

 reflector, and if the directivity pattern of the source For a circular piston with axis along the line joining 

 is given by I(0)/I n where 1(9) is the intensity pro- source and receiver, 

 duced at a given distance in a direction making an 

 angle with the axis of the source (assumed to be 

 along the line joining the source and receiver) and I 

 is the intensity produced at the same distance on the 

 axis, then R- in equation (5) may be put equal to 



= cos-(tan -1 — ) 



1- 



4/( 2 



d? 4- Ah- 



(10) 





■»{?"■") 



1_ A 



(11) 



