An isotropic multidimensional medium is propagating dispersive radiation from a suddenly triggered immersed point source. The latter's subsequent action is postulated as being transient. A contour integration technique accounts for a part time zero condition plus other supplementary hypotheses (e.g. that of stability), leading via the stationary phase technique to an asymptotic solution valid for large time. One set of results holds at comparably far range. In the ensuing dispersion, concentrically expanding trains of Kelvin approximated waves get emitted. These wave trains are generally bounded by spherical advancing frontal and/or rear edges near which Airy-type approximations can be made. Several such edges may coincide or almost coincide. Another set of results, involving Hankel or Bessel functions, holds at any given finite range; it indicates slow wave packets and implies, consistent with a transient source, the ultimate attainment of a steady state of silence, possibly within a 'slowest' spherical edge. Applications are illustrated for elastic plate deflexions and Klein-Gordon governed motions.