1、bosinbA1r2rr1sin2brr2sin2brrabH2H2主瓣旁瓣02701 8 0180( )( )(0)AApRpThe directivity functionRadiation of sound will be found equal to zero at certain angles from the maximum of the axial direction of the source, which is called the directivity acute angle0 (0)2AApr(0)( )cossin( )2AApbRkpsin(2sin )2sin(s
2、in )bb12sin2cossin()2AkbppptkrrWhen In these direction, We have two sound waves of same magnitude and phase , hencesin,sin(0,1,2)bmbmm1.When ( )1R1sin(0,1,2,),mmb2sin,sin(1,3,5,)2bmbmm2.When ( )0R1sin(1,3,5,)2mmbIn these direction, we have two sound waves of equal magnitude but 1800 out of phase wit
3、h each other.1kb sin12bksin(2sin )( )12sin(sin )bRbWe can obtain a polar plot of pressure( in dB) versus angular displacements as shown in the following Fig., which is the radiation pattern or directivity of this particular arrangement of two point sources.000900-10-20-30dB1b000900-10-20-30dB1b00090
4、0-10-20-30dB1b1/29 003 02 01 00d B1b32b3 02 01 00d B09 02b3020100dB090In general , the larger the extent of the radiator (here we mean the spacing between the sources), the sharper will be the major lobe and the greater the number of side lobes.()ijt kriAper()1injt kriiAperbd213211sinsin2 sin ,(1) s
5、innrrbrrbrbrrNbbd1()2(1)1110( , )1.( )jt krjjj NNjnnAp reeeerp re 1()11( )jt krAp rerkbsinN1120sin()121sin()2NjNnjjnjnNeeee 11()2()sin()2sin()2sin()2sin()2Njt krjt krNAperNAer()(0)jt krApNersin ()sin( )( )(0)sin ()sinNbPRbpN0bNbdsinsinsinbbsinsin( )()sindRd134,1,222dN9003020100dB12d9003020100dB1d9003020100dB32d9003020100dB2d
