  We present an experimental study of the mechanical impulse propagation
through a horizontal alignment of elastic spheres of progressively decreasing
diameter $\phi_n$, namely a tapered chain. Experimentally, the diameters of
spheres which interact via the Hertz potential are selected to keep as close as
possible to an exponential decrease, $\phi_{n+1}=(1-q)\phi_n$, where the
experimental tapering factor is either $q_1\simeq5.60$~% or $q_2\simeq8.27$~%.
In agreement with recent numerical results, an impulse initiated in a
monodisperse chain (a chain of identical beads) propagates without shape
changes, and progressively transfer its energy and momentum to a propagating
tail when it further travels in a tapered chain. As a result, the front pulse
of this wave decreases in amplitude and accelerates. Both effects are
satisfactorily described by the hard spheres approximation, and basically, the
shock mitigation is due to partial transmissions, from one bead to the next, of
momentum and energy of the front pulse. In addition when small dissipation is
included, a better agreement with experiments is found. A close analysis of the
loading part of the experimental pulses demonstrates that the front wave adopts
itself a self similar solution as it propagates in the tapered chain. Finally,
our results corroborate the capability of these chains to thermalize
propagating impulses and thereby act as shock absorbing devices.
