波的多普勒效应是指，波源与观察者相对运动时，观察者接收频率与波源发射频率不同的现象。多普勒效应目前在各个领域应用广泛，但理论部分内容较为零散，因此本文将整合多普勒效应相关的研究背景及结论，推导声波和光波的多普勒效应公式，对比两者的横向多普勒效应和纵向多普勒效应，使用两种方法验证光波的多普勒效应只与相对速度有关。基于之前的讨论进行延伸，在光波方面，通过将相对论情形下的多普勒效应公式进行数学上的近似，回归经典时空观；在声波方面，简要分析了超音速的声波多普勒效应。

The Doppler effect refers to the phenomenon that the frequency received by the observer is different from the frequency transmitted by the source, when the source is moving relative to the observer. At present, Doppler effect is widely used in various fields, but the theoretical content is scattered. Therefore, this paper will integrate the research background and conclusions related to Doppler effect, deduce the Doppler effect formula of sound and light, compare the transverse Doppler effect and longitudinal Doppler effect, verify that the Doppler effect of light is only related to the relative velocity by using two methods. Based on the previous discussion, in the aspect of light, using mathematical approximation, the Doppler effect formula in the relativistic case back to the classical space-time view. In the aspect of sound, the Doppler effect of supersonic sound wave is briefly analyzed.