Abstract: 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.

Key words: general Lorentz transformation, general Doppler effect, effective wave speed, general principle of phase invariance, wave pulses