Fixed-path-length cylindrical cavities for redetermining the Boltzmann constant

In preparation for re-determining the Boltzmann constant k_B at NIM, we report studies of the longitudinal acoustic resonances in five, argon-filled, fixed-path-length cylindrical cavities. These cavity resonators differ in lengths, method of support, and gas fill ducts. The square of the apparent speed of sound c² in each cavity deviates from reference values by linear functions of the pressure with mode-dependent, negative coefficients. Thus, all the resonators are more compliant than our models predict. The best-performing resonator was 80 mm long and 80 mm in diameter. For this resonator, the zero pressure limits of c² for the four modes had a fractional standard deviation from their mean of 3.6×10⁻⁶. This suggests that we can reduce the uncertainty of our previous measurement of k_B by a factor of two.