Quasinormal spectra of a wormhole family: overtone features and a parameter-controlled redshift

Though investigated extensively in the past, we take a detailed relook at the study of quasinormal modes (QNM) in a known family of wormholes (ultrastatic ($g_{00}=-1$), as well as spacetimes with different, non-constant $g_{00}$), which includes the familiar Bronnikov-Ellis spacetime as a special case. Our focus here is to go beyond the fundamental mode and obtain some of the QNM overtones using a suitable numerical scheme. Scalar and axial gravitational QNMs including two or three overtones are obtained for the family of ultrastatic geometries and their parameter dependencies are shown explicitly. Further, we comment on how (a) the overtones may influence the time-domain profile in a perturbation and (b) in what sense, the use of overtones may help in distinguishing between different geometries within the family. Finally, we show how an effect somewhat similar to the so-called `environment induced redshift' of QNMs, introduced recently (Phys. Rev. D \textbf{111}, 064026 (2025)), may be obtained for spacetimes with non-constant $g_{00}$, via an appropriate tuning of available metric parameters which systematically modify the shapes of the effective potentials arising in the perturbation equations.