  We investigate the waveforms and quasi-normal modes around Schwarzschild
traversable wormholes under different field perturbations, including the scalar
field perturbation, the electromagnetic (vector) field perturbation and the
gravitational (tensor) field perturbation. By comparing Schwarzschild
traversable wormholes with Schwarzschild black holes, we find some unique
properties for the former. At first, the perturbation waveform includes echoes
and damping oscillations around Schwarzschild traversable wormholes, while it
has only the damping waveform around Schwarzschild black holes. Secondly, the
difference between adjacent peaks of echoes varies with the mass parameter and
the defect parameter in the waveform around Schwarzschild traversable
wormholes, while it always keeps constant around Schwarzschild black holes.
Thirdly, the ordinary isospectrality between the odd and even parities no
longer exists in the quasi-normal modes of gravitational perturbations around
Schwarzschild traversable wormholes, but an alternative isospectrality appears.
According to these properties, we summarize a scenario for estimating the mass
parameter and the defect parameter of Schwarzschild traversable wormholes
through the waveforms and quasi-normal modes. Our analyses provide a more
profound comprehension of the inherent characteristics of Schwarzschild
traversable wormholes.
