We investigate the second order gravitational waves induced by the primordial
scalar and tensor perturbations during radiation-dominated era. The explicit
expressions of the power spectra of the second order GWs are presented. We
calculate the energy density spectra of the second order GWs for a
monochromatic primordial power spectra. For large $k$ $(k>{k}_{\ast})$ ,
the effects of the primordial tensor perturbation with tensor-to-scalar ratio
$r={A}_{h}/{A}_{\zeta}=0.2$ lead to an around $50\mathrm{\%}$ increase of the
signal-to-noise ratio (SNR) for LISA observations.