Effect of viscosity on longitudinal vibrations in bars.—The theoretical development is based on the assumption, due to Stokes, that the stress in the medium due to viscosity is proportional to the first power of the time rate of shearing strain. The equation of propagation of a plane longitudinal sound wave along a slender bar is made to include the viscous stress which arises from the shearing strain associated with this type of disturbance. Comparison with experiment. Specimen bars are excited to longitudinal vibration by means of a high frequency, sinusoidal alternating electric field impressed on a piece of piezo-electric quartz cemented to one end of the bar. The amplitude of vibration is observed by measuring the torque on a Rayleigh disk suspended in air immediately off the other end of the bar. Resonance curves are obtained showing the relation between the square of the particle velocity at the end of the bar and the frequency of excitation. The experimental curves for hard drawn copper, aluminum, and glass are in admirable agreement with those deduced from the theory. Curves for soft annealed copper and silver, however, exhibit discrepancies which indicate the presence of viscous forces varying according to higher powers of the strain velocity.

Coefficient of viscosity as determined from longitudinal vibrations.—Where the agreement is good, comparison of the observed with the theoretical resonance curves yields the value of the coefficient of viscosity of the substance multiplied by $1+\sigma$, where $\sigma$ is Poisson's ratio. The values obtained for this quantity for Al, Cu, and plate glass, are 545, 2880 and 2440 c.g.s. units, respectively. These are in the neighborhood of ${10}^3$, in marked disagreement with the values of ${10}^8$ obtained by other investigators using quite different methods. It is possible that irreversible changes involving dissipation of energy take place in slow bending which are absent in rapid vibrations.

Velocity of sound in solids.—For aluminum, hard drawn copper and plate glass the values obtained from the resonance frequencies are 5070, 3650 and 5710 m/sec., accurate to about 1 per cent.

Measurement of small changes of elasticity of bars.—Changes of less than.01 per cent can be detected by this method.

Differential frequency meter for measuring small changes of frequency in a high frequency generating set is described, sensitive to a change of less than 1 cycle per sec. in a frequency of 50,000.

Close

PrevNext

View figure in article