Doppler shift induced crosstalk (DSC) is an intrinsic type of channel crosstalk in an ultra-weak fiber Bragg grating (uwFBG) based distributed acoustic sensing (DAS) system, and has significant impact on the system's sensing performance. This paper studies the characteristics of DSC in an uwDAS system. The origin of DSC is theoretically analyzed. Accordingly,the relationship between DSC and vibration induced phase signal is derived, which reveals that the amplitude of the DSC is linearly proportional to the frequency of the phase signal. Furthermore, the irrelevance of amplitude and channel distribution is demonstrated. The uwDAS system has been constructed and the aforementioned theoretical outcomes have been confirmed through experimentation. The work presented in this paper provides a theoretical foundation for a more profound comprehension of crosstalk and its mitigation in uwDAS systems.