  Damour-Solodukhin wormholes are intriguing theoretical constructs, closely
mimicking many properties of black holes. This study delves into two distinct
characteristics of the waveforms emitted from such wormholes, namely, the
late-time tails and echoes, which can substantially be used to distinguish its
identity. Notably, both features appear in the latter stages of quasinormal
oscillations and stem from the singularities of the Green's function. The
late-time tail, on the one hand, arises due to the branch cuts in the relevant
Green's function. Within the Damour-Solodukhin wormhole paradigm, singularities
are present in both ingoing and outgoing waveforms, which entails a
generalization of the existing recipe for black hole metrics. On the other
hand, the echoes are attributed to a new set of quasinormal poles,
supplementing those of the respective black holes, reminiscent of the scenario
where the spacetime metric possesses a discontinuity. It is inferred that both
features are observationally relevant in distinguishing a wormhole from its
black hole counterpart. Moreover, we suggest a potential interplay concerning
the late-time evolution between the two mechanisms in question.
