  It has been recently shown that observing pulses isolated from the
gravitational radiation transient (also known as echoes) would prove the
existence of exotic compact objects (ECOs). Many features of the ringdown
signal can be reproduced by simulating a scattering problem instead of the full
coalescence of ECOs. In this paper, we study the dynamics of scalar and tensor
wavepackets colliding against a spherically symmetric Morris-Thorne wormhole.
Our aim is to extract the features of the time-dependent scattering solutions
inside and outside the effective potential cavity in addition to their
asymptotic behavior. Using the geometrical optics approximation, we show that
the amplitude of the echoes is only large enough in a narrow bandwidth of
frequency space. Additionally, we show that the cavity modifies the
polarization of the asymptotic gravitational wave solutions. The computer code
used to produce these results is publicly available for further applications,
including scattering and accretion processes.
