Geodesic
The application of the matrix Riemann problem to the investigation of normal waves excitation in an acoustic
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 129-132

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Stationary excitation of normal waves in a flat acoustic waveguide with absolutely soft lateral walls by a piston radiator is investigated. The massive radiator located in a center of the waveguide is supported by anelastic spring. Exact analytical solution is obtained for the case, when the radiator length is equal to one-half width of the waveguide. The solution of this problem is reduced to the matrix Riemann problem. The matrix of the Riemann problem admits effective factorization by quadratures. The representation of the acoustic field in the waveguide in the form of the normal waves expansion is given. The normal wave amplitudes and the acoustic fields excited in the waveguide by the radiator are studied analytically. 
@article{ZNSL_1997_239_a11,
     author = {V. D. Luk'yanov},
     title = {The application of the matrix {Riemann} problem to the investigation of normal waves excitation in an acoustic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--132},
     publisher = {mathdoc},
     volume = {239},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a11/}
}
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V. D. Luk'yanov. The application of the matrix Riemann problem to the investigation of normal waves excitation in an acoustic. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 129-132. http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a11/