  Cosmological stochastic gravitational waves (GWs) induced by a spectator
field are usually expected to have an amplitude very small compared with those
generated by the curvature perturbation, or equivalently by a field dominating
the universe. On the contrary to this expectation, we show that a spectator
field that provides a tensor perturbation, on top of the metric tensor
perturbation, can generate a significant amount of GWs. The amplitude and
frequency of the generated GWs may lie within the sensitivity range of future
GW detectors. In particular, if the sound velocities of the two tensor
perturbations coincide, the induced GW amplitude may become very large due to
resonance by forced oscillation, even in the limit of small coupling between
them. A distinct feature of this scenario is that, since tensor modes can
hardly lead to the formation of primordial black holes (PBHs), we expect no
presence of PBHs, in contrast to the usual scalar-induced case, in which the
detection of strong enough induced GWs suggests the existence of PBHs.
