This paper studies the'scattering interaction o fan incident acoustic pulse and an elastic target. The pulse emerges from a distant transducer and can have any arbitrary shape and finite duration. The target is an elastic body. here assumed to be spherical and homogeneous. The Fourier integral representation of the incident pulse is combined with the resonance-scattering representation of the scattered pressure field to yield a filter-type integral that can be viewed as filtering the form function of the scatterer through the spectral window of the incident transient pulse (ping). We anal.roe the backscattered pulses when the incident pulses are of three simple types. The analysis is carried out in the frequency and time domains, and results are illustrated with numerical predictions for a variety of instances of increasing complexity and interest. The nature of the backscattered echo is explained in two instances for either short or long pulses. These instances correspond to cases in which the incident pulse has a carrier frequency that either coincides with an)' o.f the natural resonances of the submerged sphere or not. The main advantage of short pulses is that the)" can be used to replicate the (stead)" state) sonar cross-section of scatterers. Ultimately, if the incident pulse were a delta function in r, the spectrum of the backscatteredpulse would exactly be the form function f~(n, x) divided by r. The backscattering sonar cross-87