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Published online by Cambridge University Press: 15 July 2019
The thin tube theory for a sausage wave is developed from first principles and shown to lead to the Klein-Gordon equation. The equations that hold when gravity is negligible are explored and the dispersion relation obtained and compared with earlier results. The effects of stratification are explored in detail, with contributing terms to the cutoff frequency explored for various cases ranging from a rigid and straight tube to a diverging elastic tube of the shape expected for a thin flux tube. The cutoff frequency is illustrated for a range of conditions likely to arise in the solar atmosphere. The role of cutoff for coronal loops is explored.
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