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Maxwell and Acoustics
taken and retained by Charles Darwin’s son, G. H. Darwin (Harman, 1995). Max- well also reviewed Osborne Reynolds’ pa- per concerning wind-induced refraction of sound for the Proceedings of the Royal Society (Harman, 2002).
Support for the Kinetic Theory from Acoustics of
a Monatomic Gas, 1876
Up to the mid-1870s, it remained difficult to understand the measured values of γ = cp/cv for any gas, the weakness of the ki- netic theory noted by Maxwell at the end of his 1860 paper. Eventually, Kundt and Warburg (1876) used an acoustical mea- surement to determine γ for mercury va- por to be 1.666, a value consistent with the kinetic theory combined with a proper interpretation of the nature of the gas mol- ecules.
It is first appropriate to explain the tech- nique Kundt developed in the late 1860s for visualizing acoustic standing waves in gases confined in a glass tube. Figure 4 shows a “Kundt tube” as depicted in a gen- eral textbook. A long solid rod is support- ed near its midpoint by a stopper (K-K). The rod is set into longitudinal vibrations by rubbing the rod, and the associated vi- brations of the metal plate (a) at the end of the rod set up acoustic standing waves in the gas within the glass tube held in a horizontal position. Kundt found that when a light powder was present on the floor of the glass tube, the powder would move and accumulate in bands separated by a spacing of half a wavelength for the acoustic wave in the gas.
Figure 4. Diagram of Kundt’s method for measuring the wavelength of sound scanned from Atkinson (1890). Sound waves driven in the gas by the oscillating plate (a) are reflected from an adjustable stopper (b). The resulting standing acoustic wave in the gas causes powder to accumulate at regularly spaced intervals as depicted in this diagram.
The experiment published in 1876 was more sophisticated due to the properties of mercury vapor. To motivate their measurements, Kundt and Warburg explained “there is cur- rently an unresolved contradiction between experiment and theory” (in translation), indicating that it would be help- ful to measure γ for a monatomic gas. Mercury vapor was proposed for investigation because it was interpreted as monatomic, provided hydrogen gas was viewed as diatom- ic. Either they or a colleague (Herr Baeyer, who suggested considering mercury vapor) was aware of the suggestion promoted by Cannizzaro in 1860 that molecular weights needed to be reinterpreted by assuming hydrogen gas to contain only diatomic molecules. Kundt and Warburg re- duced the uncertainty in their measurement by comparing wavelengths measured at the same frequency for mercury vapor (at a known elevated temperature) with that of air at a known temperature. Consequently, their determination of γ for mercury relied on separate accurate results for the value of γ for air that had recently become available. In their application of kinetic theory, they interpreted mercury va- por as consisting of smooth spherical atoms not possessing rotational kinetic energy such that Maxwell’s parameter in Equation 2 becomes β = 1 so that they predicted γ = 5/3, in agreement with their measurements.
We can be confident of Maxwell’s early appreciation of Kundt and Warburg’s result because of a postscript he con- tributed to an obscure publication (Preston, 1877). It is first appropriate to introduce the author, S. Tolver Preston (1844- 1917). One of Maxwell’s London collaborators in electrical measurements was Fleeming Jenkin, also an assistant of William Thomson (later known as Lord Kelvin) in the en- gineering of long-distance telegraphy. Preston had assisted Thomson and Jenkin with telegraphy, although by the mid- 1870s, he was in need of employment. Maxwell was favor- ably disposed toward Preston, indicating in a letter to P. G. Tait (another mutual friend) in December 1876, “[Preston] has really a good head if it were only trained a little and is no paradoxer” (Harman, 2002, p. 551). Preston had written Maxwell on December 5, 1876, evidently enclosing a manu- script of much of the publication (Preston, 1877). In his let- ter as well as in his publication, he endeavored to examine qualitative relationships between c, the speed of sound in gases, and the kinetic theory of gases (Garber et al., 1986). Preston’s publication is important because of a second post- script, designated as P.S. (2), containing results “worked out mathematically” by Maxwell and an associated mention of
26 | Acoustics Today | Winter 2016