LOUD SPEAKERS AND MICROPHONES 



277 



In all practical types of loud speakers kh cos kh/sln kh would be 

 very nearly equal to 1 ; then 



pel 



w 



1 



kw 





X = — 



pd 

 h 



kl 



+ COt2 kl 

 1 



cotkl + [~ ] tan kl 



w 



kW 



If the total area of the diaphragm is A and that of the corresponding 

 channels a, then Aja = l/iu, approximately, and the total impedance 

 becomes 



pcA^ 1 



/ kh \ 2 



( — j A^ -\- kT- cot2 kl 



X = - J 



pcA 



1 - 



1 



kl cot kl -\- [ J - I kl tan kl 



References 



1. "Absolute Amplitudes and Spectra of Certain Musical Instruments and Orches- 



tra," L. J. Sivian, H. K. Dunn, and S. D. White. Jour. Acous. Soc. Am., 

 V. 2, Jan. 1931, p. 330. 



2. "Audible Frequency Ranges of Music, Speech, and Noise," W. B. Snow. Jo74r. 



Acous. Soc. Am., v. 3, July 1931, p. 155. 



3. Backhaus, Zeits. f. Tech. Physik, v. 9, 491, 1928. 



4. "Engineering Acoustics," L. E. C. Hughes, p. 47. Benn, London. 



5. W. J. Albersheim and J. P. Maxfield, similar relations were presented in a paper 



before the Acoustical Society in May 1932. 



6. "Sur la Propagation des Ondes Sonores d'Amplitude Finie," M. Y. Rocard. 



Comptes Rendus, Jan. 16, 1933, p. 161. 



7. "Theory of Vibrating Systems and Sound," Crandall. P. 163 ff. D. Van Nos- 



trand. New York. 



8. "Moving Coil Telephone Receivers and Microphones," E. C. Wente and A. L. 



Thuras. Jour. Acous. Soc. Am., v. 3, 1931, p. 44. 



9. " E.xtraneous Frequencies Generated in Air Carrying Intense Sound Waves," 



A. L. Thuras, R. T. Jenkins and H. T. O'Neil. To be presented at mtg. of 

 Acous. Soc. Am., April 30-May 1, 1934. 



