84 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



L to be lengthened by the amount AL, and since AL/L = ajY 

 ( Y, Young's modulus of elasticity) , the natural frequency can be 

 expressed by 



f = 22A 7 T ^ 



Any change of the length or of the force or of the stress in the wire 

 causes a corresponding change of the natural oscillation frequency of 

 the wire. 



The mechanical oscillation of the wire is converted into an electric 

 signal usually by means of an inductive pickup system P located 

 near the oscillating string. The (steel) wire, in vibrating, varies the 

 magnetic flux in the air gap of the pickup system; the output signal 

 is amplified and fed back into an electromagnet M to keep the string 

 excited in its natural frequency. 



The transducer has been used for a range of stress in the string 

 between 20 and 60 kg/mm 2 . If the stress becomes too low (i.e., lower 

 than 15 kg/mm 2 ) the wire generally will not produce a pure sinusoidal 

 oscillation; if the stress is too high, it will exceed the limit of pro- 

 portionality. The maximum displacements that can be measured 

 are of the order of one-thousandth of the wire length. The minimum 

 displacement that can be observed can be very small, since frequency 

 deviations can be measured with a high amount of sensitivity. It has 

 been claimed that displacements as low as 0.1 /u can be detected. 



The error of the method is, in general, between 0.1 and 1 per cent. 

 The frequency variation is a nonlinear function of the displacement 

 or the force as evident from Eqs. (l)and (2). The process to be investi- 

 gated must be long compared to the oscillation period of the wire; 

 variations occurring in j^q of a second have been measured. 1 



The natural frequency of the wire varies strongly with tempera- 

 ture. A variation of temperature from to 40°C causes the same 

 variation in the output as does a change in stress by 10 kg/mm 2 . 

 Thermal compensation by mounting the wire on a base with the same 

 thermal expansion coefficient as the wire is frequently required. The 

 length of the string is in general between 20 and 200 mm ; if it is too 

 short, end conditions become too important and the relationships of 

 Eqs. (1) and (2) are no longer valid. A ratio of length to wire diameter 

 of more than 250 is recommended. 



The oscillating-string transducer is primarily applicable for large 

 forces. If thermally protected, its long-time operating stability can 



1 H. Moser, Bull, schiveiz. elektrotech. Ver., 25, 689 (1934). 



