The weakly nonlinear propagation of a pulsed sound beam generated by a real sound source in a homogeneous fluid is considered. The investigation is based on the weakly nonlinear approximation of the Khokhlov–Zabolotskaya–Kuznetsov nonlinear parabolic equation. It is discussed how diffraction and absorption alter the pulse. Analytical and numerical solutions are presented, and the validity of older models on the self‐demodulation of a pulsed signal is discussed.