Doppler effects in periodic acoustic media were studied theoretically and experimentally. Analytical formulas are derived using the Green's function formalism. We found that a far field observer cannot hear the sound inside a band gap from a stationary source, but a moving source can be heard even if the frequency is inside the gap, and the Doppler shifts can be inverted or anomalously large.
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Hu et al. (2006) studied this question.
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