Fig. 1. Photo of temperature sensor prototype. 



of the mass of the disc to the area of the post. 

 The practical minimum time constant is not deter- 

 mined by the resonator, however, but by the fre- 

 quency counter. A counter requires a minimum 

 of 10 seconds to count a 36 Kcps frequency to 

 the required 6 places; it is probable that the 

 temperature time constant of the resonator can 

 be reduced to match this. 



MATHEMATICAL EXPRESSION 



The expression for a thin disc with no post 

 and vibrating flexurally with two nodal diameters 

 is 



f = 



0.238 t 



/ 



Y 

 e(l-c^) 



(1) 



where f is resonator frequency in cps, R the 

 radius of the disc in cm, t the thickness in cm, 

 Y is Young's modulus in dynes/cm^, o Is Poisson's 

 ratio and e the mass density in gm/cm3. The 

 change in Young's modulus with temperature 

 accounts for most of the frequency changes, Y 

 changes about 0.0l($ for each degree Centigrade 

 change. The frequency changes due to expansion 

 alone are of an order of magnitude less. Varying 

 the thickness to diameter ratio changes the disc 

 frequency, as the expression indicates, but the 

 mode of operation is lost as the thickness- 

 diameter ratio approaches one. The expression 

 becomes inaccurate as the disc becomes thicker 

 and with the addition of posts. 



36 



