Geodesic
High frequency wave field of the source moving in the wavequide
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 71-78

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The problem of the moving source wave field is considered in the regular waveguide with perfectly reflected boundaries. It is supposed that the acceleration of the source is small. The asymptotics of acoustical field is constructed in the special moving coordynate system. It is shown, that in the case when Doppler frequency of the source is equal to the critical frequency of mode under consideration this asymptotics is invalid. New asymptotics in the neighbourhood of such critical cross-section is constructed. 
@article{ZNSL_1997_239_a5,
     author = {V. S. Buldyrev and A. V. Sokolov and A. S. Starkov},
     title = {High frequency wave field of the source moving in the wavequide},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {71--78},
     publisher = {mathdoc},
     volume = {239},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a5/}
}
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V. S. Buldyrev; A. V. Sokolov; A. S. Starkov. High frequency wave field of the source moving in the wavequide. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 71-78. http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a5/