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The method of the statistical energy analysis (SEA) has become a useful technique to predict the sound insulation and structural vibration in buildings. The accuracy of the prediction depends on the model of interaction of waves of different types and wave transmission through joints of structural elements. The method of SEA requires exact calculations of modal densities of waves of different types in structures. At high frequency, the correction based on the theory by Rayleigh, R.D. Mindlin and J.H. Rindel gives more accurate dispersion relations for phase velocities of longitudinal and bending waves in thick beams and plates.