The influence of the frequency chirp inherent to the generation of a pump pulse by a Mach-Zehnder intensity modulator is presented in the context of a distributed Brillouin sensor configuration. This frequency chirp depends on the pulse shape and its impact is related to the relative importance of the rising and falling edges with respect to the total pulse width. This results in a biased evaluation of the Brillouin frequency in regions where an abrupt change of this Brillouin frequency is observed.