一般多普勒效应的综合统一分析

The comprehensive and unified analysis of the general Doppler effect

在物理学教材中分别给出了声波和光波的多普勒效应公式,但两者表达式不同.一些文献分析了两者间的联系,但没有真正地将两者统一起来;另一些文献虽作了统一分析,但均在特殊洛伦兹变换下讨论问题,所得结果又不具有一般性.本文在不区分声波与光波的情况下,基于波动传播的共同本质,综合运用多种方法导出一般多普勒效应的表达式,系统地论证两者的统一性.通过分析得到了一般多普勒效应的3个等价表达式,而教材中声波与光波的多普勒效应公式乃是其不同情况下的特例.

The Doppler effect formulae of sound wave and light wave are given respectively in physics textbooks,but the two expressions are different.Some literatures analyze the connection between the two,but it does not really unify the two;although other literatures are uniformly analyzed,but they are all discussed based on the special Lorentz transformation,and the results are not general.In this article,without distinguishing between sound wave and light wave,based on the common essence of wave propagation,the expressions of the general Doppler effect are derived by multiple methods to systematically demonstrate the unity of the two.Though analysis,three equivalent formulae of the general Doppler effect are obtained,and the Doppler effect formulae of sound wave and light wave in physics textbooks are special cases of different situations.