TRANSMITTING 



25 



one, or between two, of the curves oi the family <>l 

 curves drawn on the chart. Suppose, for example, 

 that this point falls about 7/10 of the way between 

 the curves corresponding to 0.003 and 0.004. Then 

 for the angle « 



In 



sin a = 0.0037. 



The values of /„//„ sin a may be qui< kly obtained for 

 each desired value of the angle a. These are then 

 plotted as described above. The procedure beyond 

 this point is identical with that described earlier. 

 The use of this chart at USRL has indicated that it 

 is as accurate in general as a direct computation and 

 the work proceeds much more quickly, particularly 

 since most field data for instruments give directly 

 10 log/ a //„ rather than / a //„. 



In the above, it is assumed that the pattern has 

 been drawn with the maximum on the outer circle on 

 the coordinate paper. If the maximum is drawn on 

 the circle which is 10 db down, the chart may still 

 be used in the same way, but the values obtained for 

 /„//„ sin a from the chart should be multiplied by 10 

 to obtain the correct values; if the maximum is on 

 the circle 20 db down, the chart values must be mul- 

 tiplied by 100, etc. 



The chart can also be applied to a line. In this case 

 it is turned so that 90 degrees on the chart coincides 

 with degrees on the directivity pattern. Since the 

 chart in that direction is narrower, it will be neces- 

 sary to plot the pattern on a smaller scale in order 

 that the chart may accommodate it. 



If the beam width is not too broad (total beam 

 width 10 db below peak does not exceed 120 degrees), 

 and the side lobes and rear response are at least 15 db 

 below the peak, the directivity index is practically 

 determined by the beam width alone. Thus, in Figure 

 7 the directivity index is plotted for a circular plate 

 as a function of the beam width. By referring to this 

 chart, one may read directly the directivity index for 

 the measured beam width. 



Many devices do not have directivity patterns sym- 

 metrical about a single axis. In general, then, direc- 

 tivity patterns would have to be measured in a great 

 many planes passing through the acoustic axis, and 

 a laborious double numerical integration performed 

 to obtain the directivity index. In some cases where 

 the pattern is symmetrical with respect to two per- 

 pendicular planes passing through the acoustic axis, 



20 40 60 80 100 120 140 160 

 BEAM WIDTH IN DEGREES (I0DB DOWN) 



180 



Figure 7. Directivity index as a function of the beam 

 width lor a circulai plate. 



an approximate value for the directivity index may 

 be obtained by a simple procedure which requires 

 taking directivity patterns only in these two planes. 

 It is further required that the beam widths in these 

 two planes be less than 120 degrees. To illustrate this 

 method, let us consider a rectangular piston which 

 is the most commonly occurring nonsymmetrical type 

 in practice. For such a piston, the directivity index 

 given is directly determined only by the beam width 

 in the two planes and can be represented as a function 

 oi this beam width. For this case, a chart is given in 

 Figure 8, from which the directivity index can be 

 found from the measured beam width, 10 db down, 

 in the two planes. The two planes in this case are the 

 the planes passing through the acoustic axis and pa- 

 rallel respectively to the two pairs of sides of the rec- 

 tangle. A similar calculation can be made for an 

 elliptical piston when the two planes are taken 

 through the acoustic axis and parallel respectively 

 to the major and minor axes of the ellipse. A chart 

 lor this case also is given in Figure 8. These charts 

 may be used in conjunction with measured patterns 

 for rectangular or elliptical transducers. 



Consideration has been given to reduction of side 

 lobes by means of tapering. (See reference 14.) By 

 tapering is meant the variation of the velocity distri- 

 bution oxer the diaphragm of the transducer so that 

 the velocity decreases from the center to the peri- 

 phery. This method is cptite effective for reducing 

 side lobes, but it has the undesirable effect of increas- 

 ing the beam width. The methods described above 

 for calculating the directivity index can in general be 

 applied directly to tapered transducers. The effect of 



