  The phenomenon of the displacement of the position of the pressure, intensity
and acoustic radiation force maxima along the axis of focused acoustic beams
under increasing driving amplitudes (nonlinear focal shift) is studied for the
case of a moderately focused beam excited with continuous and 25 kHz amplitude
modulated signals, both in water and tissue. We prove that in amplitude
modulated beams the linear and nonlinear propagation effects coexist in a
semi-period of modulation, giving place to a complex dynamic behaviour, where
the singular points of the beam (peak pressure, rarefaction, intensity and
acoustic radiation force) locate at different points on axis as a function of
time. These entire phenomena are explained in terms of harmonic generation and
absorption during the propagation in a lossy nonlinear medium both, for a
continuous and an amplitude modulated beam. One of the possible applications of
the acoustic radiation force displacement is the generation of shear waves at
different locations by using a focused mono-element transducer excited with an
amplitude modulated signal.
