458 



BELL SYSTEM TECHNICAL JOURNAL 



to fundamental laboratory problems in the field of sound measure- 

 ments. The necessary work toward commercialization has not been 

 effected, in view of the high quality performance and certain practical 

 advantages of available types of microphones. 



APPENDIX I 



For a stretched membrane, the equation expressing the statical 

 deflection ^ as a function of the radius r, for a symmetrical distribution 

 of pressure p, is ^ 



(1) 



rdr\dr 



where r is the tension coefficient. Two integrations give 



(2) 



'HV.f. 



prdr 



dr, 



where R is the bounding radius. The central displacement is evidently 



(3) 



^0 



'i'U 



prdr 



dr. 



Now, considering the case of a progressive plane wave 



p = P cos (co/ — kx) 

 2x 



where k = 



] traveling across this membrane, an expres- 



wave-length 



sion can be computed for the average pressure on the boundary of the 

 circle of radius r. From Fig. 6 it is clear that 



X — R — r cos 6 



Fig. 6— 

 * See Lamb's " Dynamical Theory of Sound," § 54. 



