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Resonant oscillations in closed tubes

  • W. Chester (a1)

Abstract

An investigation is made of the disturbances produced in a closed, gas-filled tube by the oscillations of a piston at one end, when the piston oscillates at near resonant frequencies. Within a well-defined frequency band around each resonant frequency, shock waves appear in the solution; outside this interval the oscillations are continuous, but not purely sinusoidal.

The solution includes the effects of compressive viscosity, and of shear viscosity in the boundary layer at the walls of the tube. For typical laboratory conditions the effect of compressive viscosity is found to be quite small (giving a shock thickness of the order of 10−4in.). The boundary layer effect can be more significant, though the most important modification required of the usual acoustic theory is found to arise from the non-linear terms.

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References

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Betchov, R. 1958 Phys. Fluids, 1, 3.
Erdélyi, A. 1956 Asymptotic Expansions. New York: Dover.
Langer, R. E. 1934 Trans. Amer. Math. Soc. 37, 637.
Lettau, E. 1939 Dtsch. Kraftfahrtforsch, 39, 1.
Lighthill, M. J. 1956 Surveys in Mechanics (edited by G. K. Batchelor & R. M. Davies). Cambridge University Press.
McLachlan, N. W. 1947 Theory and application of Mathieu Functions. Oxford University Press.
National Bureau of Standards 1951 Tables Relating to Mathieu Functions. New York: Columbia University Press.
Saenger, R. A. & Hudson, G. E. 1960 J. Acoust. Soc. Amer. 32, 961.
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