The response of materials and the functioning of devices are often associated to crackling noise, which encodes fundamental physical properties of the system. The asymmetry of avalanche shapes, commonly observed in many diverse noisy phenomena, still needs an explanation. We show that such asymmetry is a direct signature of the presence of inertial effects and, in particular, of the sign of the effective mass. We present experiments on the Barkhausen effect (the noise induced in magnets by the jerky motion of domain walls as they interact with impurities) and quantitatively explain the results in terms of the propagation of eddy currents in the material. The leftward asymmetry of avalanche pulses indicates the presence of a negative effective mass for ferromagnetic domain walls. These results provide a method to determine the underlying effective mass from a generic noisy signal.