CIRCULAR MEMBRANE 



41 



circular membranes. For cases of practical interest the membrane is 

 rigidly clamped and stretched by a massive circular ring. The funda- 

 mental frequency. Fig. 3.3^, of a circular membrane is given by 



J82 / 



where m = mass, in grams per square centimeter of area, 

 R = radius of the membrane, in centimeters, and 

 T = tension, in dynes per centimeter. 



fi2 = 2.92foi 



f22-3.5ofoi 



fi3 = 4.22for 



3.5 



Fig. 3.3. Modes of vibration of a stretched circular membrane. Shaded segments are dis- 

 placed in opposite phase to unshaded. 



The fundamental vibration is with the circumference as a node and a 

 maximum displacement at the center of the circle (Fig. 3.3y^). The fre- 

 quencies of the next two overtones with nodal circles are 



/o2 = 2.30/01 

 /o3 = 3.60/o: 



