V.A.Pozdeev Violation of the solutions' superposition principle for the initial-boundary problem with the moving borders for the wave equation |
Acoustic bulletin, Vol. 4 ¹ 1, (2001) |
| By giving an example of the analytical solution of the initial-boundary problem for the acoustic wave radiation by a moving plane piston the violation of the superposition principle taking into account the moving boundaries, even in the case of a linear wave equation, is shown. The solution, developed for the piston motion, represented as the superposition of the low-amplitude oscillations upon the constant velocity, describes the known Doppler effect. All the results are obtained on the base of the method of non-linear time conversion. |
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KEY WORDS: the superposition principle, moving boundary, the Doppler effect |
| TEXT LANGUAGE: Russian |