  We investigate the scalar induced gravitational waves which propagate with a
speed different from the speed of light. First, we analytically calculate the
expression of the power spectrum of the scalar induced gravitational waves
which is based on the speed and the spectrum of the primordial curvature
perturbations. Then, we discuss several scalar power spectra and obtain
corresponding fractional energy density, such as the monochromatic power
spectrum, the scale invariant power spectrum and the power-law power spectrum.
Finally, we constrain the scalar induced gravitational waves and evaluate the
signatures of the speed from the combination of CMB+BAO and gravitational waves
observations. The numerical results are obvious to reveal the influence of
speed of scalar induced gravitational waves.
