Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Test of a virtual cylindrical acoustic resonator for determining the Boltzmann constant



XiaoJuan Feng, Hong Lin, Keith A. Gillis, Michael R. Moldover, Jintao Zhang


We report progress in determining the Boltzmann constant kB using a virtual acoustic resonator derived by combining the measured frequencies of the longitudinal acoustic modes of two argon-filled, cylindrical, cavity resonators in such a way as to minimize the effects of the cavities' ends including transducers and ducts attached to the ends. The cavities had lengths of 80 mm and 160 mm and were operated in their longitudinal (ℓ,0,0) modes. We explored virtual resonators that combine modes of the two resonators that have the nearly the same frequencies. The virtual resonator formed from the (2,0,0) mode of the 80 mm resonator combined with the (4,0,0) mode of the 160 mm resonator yielded a value for kB that is, fractionally, (0.2 plus or minus} 1.5)×10-6 larger than the 2010 CODATA-recommended value of kB. (The estimated uncertainty is one standard uncertainty corresponding to 68 % confidence level.) The same virtual resonator yielded values of the pressure derivatives of the speed of sound c in argon, (dc2/dp)T and (dc2/dp2)T that are nearly consistent with literature values even though the values of kB, (dc2/dp)T and (dc2/dp2)T from each cavity, considered separately, were not. However, combining the results from the (3,0,0) or (4,0,0) modes of shorter resonator with the results from the (6,0,0) or (8,0,0) modes of the longer resonator yielded incorrect values of kB that varied from run-to-run. We speculate that these puzzling results originated in an un-modeled coupling, either between the two cavities (that resonated at nearly identical resonance frequencies in the same pressure vessel) or between the cavities and modes of the pressure vessel.


Boltzmann constant, acoustic gas thermometer, acoustic resonator, speed of sound, virtual resonator


Feng, X. , Lin, H. , Gillis, K. , Moldover, M. and Zhang, J. (2015), Test of a virtual cylindrical acoustic resonator for determining the Boltzmann constant, Metrologia, [online],, (Accessed April 14, 2024)
Created August 18, 2015, Updated October 12, 2021