42 MECHANICAL VIBRATING SYSTEMS 



and are shown in Figs. 3.3B and 3.3C. The frequencies of the first, 

 second and third overtones with nodal diameters are 



/n = 1.59/01 



/21 = 2.14/01 



/31 = 2.65/01 



These nodes are shown in Figs. 3. 3D, 3.3E, and 3.3F. Following these 

 simpler forms of vibration are combinations of nodal circles and nodal 

 diameters. The frequency of one nodal circle and one nodal diameter, 

 Fig 3.3G, is 



/12 = 2 92/01 

 The frequency of one nodal circle and two nodal diameters, Fig. 3.3//, is, 



/22 = 3.50/ 

 The frequency of two nodal circles and one nodal diameter, Fig. 3.3/, is 



/X3 = 4.22/01 



The stretched circular membrane is used in the condenser microphone. 

 See Sec. 9.25. The fundamental resonance frequency is placed at the 

 upper limit of the frequency range. A resistive load is coupled to the 

 diaphragm for damping the response in the neighborhood of the funda- 

 mental resonance frequency. This resistance is incorporated in the back 

 plate which serves as the stationary electrode. 



A stretched circular membrane is also used in all types of drums. In 

 this case the air enclosure as well as the characteristics of the membrane 

 controls the modes of vibration. 



3.5. Circular Clamped Plate ^^' ^^' ^^' i^- ^^ — Consider a plate under no 

 tension, uniform in cross section and rigidly clamped by a massive 

 circular ring. The fundamental frequency, Fig. 3.4yf, of a circular plate 

 is given by 



_.467/ / ^ 



" Rayleigh, " Theory of Sound," Macmillan and Co., London. 

 12 Morse, " Vibration of Sound," McGraw Hill Book Co., New York, 

 ^^ Wood, " A Text Book of Sound," Bell and Sons, London. 

 ^^ Crandall, " Theory of Vibrating Systems and Sound," D. Van Nostrand 

 Co., New York. 



^^ Lamb, " Dynamical Theory of Sound," E. Arnold, London. 



