  There is a growing expectation that the gravitational wave detectors will
start probing the stochastic gravitational wave backgrounds in the following
years. We explore the spectral shapes of gravitational waves induced to second
order by scalar perturbations and presumably have been produced in the early
universe. We calculate the gravitational wave spectra generated during
radiation and kination eras together with the associated primordial black hole
counterpart. We employ power spectra for the primordial curvature perturbation
generated by $\alpha$-attractors and nonminimal derivative coupling inflation
models as well as Gaussian and delta-type shapes. We demonstrate the ability of
the tensor modes to constrain the spectrum of the primordial curvature
perturbations and discriminate among inflationary models. Gravitational wave
production during kination and radiation era can also be distinguished by their
spectral shapes and amplitudes.
