The Tube-Correction in Measurements of the Velocity of Sound in Gases

Abstract

The evidence concerning the validity of the Helmholtz-Kirchhoff equation $\frac{\ensuremath{\Delta}V}{{V}_{0}}=\frac{[\frac{{\ensuremath{\eta}}^{\frac{1}{2}}+{(\frac{\ensuremath{\kappa}}{{C}_{v}})}^{\frac{1}{2}}(\ensuremath{\gamma}\ensuremath{-}1)}{{\ensuremath{\gamma}}^{\frac{1}{2}}}]}{D{(\ensuremath{\pi}\ensuremath{\nu}d)}^{\frac{1}{2}}}$ for the change in velocity of sound in a tube, in terms of the viscosity, thermal conductivity of the gas, diameter of tube and frequency of the sound, including some tests by existing data not hitherto utilized for this purpose, is summarized and discussed in this paper. The indications are that the equation is correct, within the limits of error, at the higher frequencies and larger tube-diameters usually employed in present day measurements. Under such conditions, this method of correction appears to be the most reliable available. A convenient approximate expression is deduced for the variation of the correction with temperature, and the constants required for its application calculated for several gases. At low frequencies and for small tubes, as commonly employed in the older measurements, the adequacy of the Helmholtz-Kirchhoff equation is not established. Partly for this reason and partly because they may correct other errors, the methods of correction that depend upon the inverse diameter law are to be preferred under these conditions, and perhaps in all cases where enough precision of measurement is obtainable. On the other hand, the system of tube-calibration by measurements with a standard gas, especially as applied in much recent work at high temperatures, is in practice particularly subject to large errors, and is theoretically justified only if the Helmholtz-Kirchhoff equation is correct.