On the Characteristics of Electrically Operated Tuning Forks

Synopsis.—A series of experiments was performed to determine the conditions affecting the period of an electrically operated tuning fork with the following results: (1) The more massive the base of the fork and the table upon which it is placed the smaller is the period. This effect, however, is not greater than one part in 10,000. (2) A change in the constants of the electrical circuit containing the electromagnet affects the period. The effect is less than one part in 10,000 for moderate changes necessary for keeping the amplitude of vibration constant. (3) The period increases linearly with the increase in the length of the gaps between the contact springs and contact points. For the forks used this increase was about one part in 500 for a change of 0.1 mm. in the length of the gaps. (4) For a given fork there is an amplitude at which the period has a stationary value. This may be a maximum or a minimum depending upon the arrangement of the mounting of the contact springs. At small amplitudes the change in the period due to a variation in the amplitude may be considerable. (5) The temperature effect increases from 1.04 × ${10}^{-4\mathrm{}}$ at - 25° C. to 1.43 × ${10}^{-4\mathrm{}}$ at 56° C. The values corresponding to temperatures above 0° C. are from 20 to 40 per cent. greater than those obtained by other observers. There are no other published data giving the temperature effect below 0° C. (6) By keeping the temperature, the length of the gap and the amplitude constant, a well-made fork can be relied upon to give a constancy of rate accurate to one part in 50,000. (7) The theoretical expression for the period of vibration of a bar holds good for a tuning fork. (8) The velocity of sound in the steel of which the forks used were made is 5.49 × ${10}^5$ cm. per sec. (9) The coefficient of modulus of elasticity of the steel is 19.10 × ${10}^{11}$. (10) The temperature coefficient of the modulus of elasticity increases from - 2.2 × ${10}^{-4\mathrm{}}$ at - 25° C. to - 2.96 × ${10}^{-4\mathrm{}}$ at 56° C. These values were computed from the relation $\epsilon =-(2\mathrm{}\theta +\alpha )$, where $\epsilon$ is the temperature coefficient of modulus of elasticity, $\theta$ the temperature effect upon the period of the fork, and $\alpha$ the coefficient of linear expansion of steel.