  We explore the possibility of multi-parametric resonances from time varying
sound speed during cosmological inflation. In particular, we fix our set-up to
the simpler case beyond a single oscillation model already explored in
literature: two sinusoidal harmonics around a constant sound speed equal to
one. We find that, within the perturbative regime, except for some certain
extreme corners of the parameter space, the primordial density spectrum is
characterized by two groups of amplified peaks centered around two critical
oscillatory frequencies of the sound speed. As a general result, we show that
the energy spectrum of the secondary induced GWs from the inflationary era has
a single major broad peak, whereas the one from the radiation dominated phase
consists of one/two principle peak-like configuration(s) for relatively
small/large ratio of two oscillatory frequencies. The GW relic stochastic
backgrounds carry a gravitational memory of the parametric resonances during
inflation. GW signals from double sound speed resonances can be tested in
complementary channels from Pulsar-timing radio-astronomy, space and
terrestrial GW interferometers.
