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In this study, irregular reflection of weak acoustic shock waves is investigated both experimentally and numerically for spark-generated spherically divergent N-waves reflecting from a plane rigid surface in air. Two optical methods are used in the measurements: a Mach-Zehnder interferometer for reconstructing the pressure waveforms and a Schlieren system for visualizing the shock front geometry. In simulations, axisymmetric Euler equations are solved for an acoustic source introduced as a Gaussian-envelope energy injection and a rigid wall as a boundary condition. Waveforms obtained in simulations are in a good agreement with those measured by the interferometer. The Mach stem formation is observed close to the surface resulting from the collision of the incident and reflected front shocks of the N-wave and further away from the surface where the reflected front shock interacts with the incident rear shock. It is shown that irregular reflection occurs in a dynamic way and the length of the Mach stem increases following a parabolic law while the N-wave propagates along the surface. Work supported by RSF-17-72-10277 and the Labex CeLyA of Universit ́e de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007).