  Recently, we have shown that the propagation speed $c_T$ of the primordial
gravitational waves (GWs) might be nontrivially varying during inflation, which
could induce local oscillations in the power spectrum of primordial GWs. In
this paper, we numerically confirm that, although with a disformal redefinition
of the metric the nontrivial $c_T$ may be set as unity, the power spectrum in
the frame with $c_T=1$ is completely the same as that in the original disformal
frame, i.e., the oscillating shape in the power spectrum is still reserved,
since here the effect of $c_T$ is actually encoded in the nontrivially varying
Hubble parameter. In addition, we also clarify how to obtain a blue-tilted GWs
spectrum by imposing a rapidly decreasing $c_T$ during inflation.
