  We have measured the electrodynamic properties of Y_{1-x}Pr_xBa_2Cu_3O_7
single crystal thin films as a function of temperature using coherent
THz-time-domain spectroscopy. We obtain directly the complex conductivity
$\sigma=\sigma_1+i\sigma_2$, the London penetration depth $\lambda_L$, the
plasma frequency $\omega_p$, and the quasiparticle scattering rate $1/\tau$. We
find that $1/\tau$ drops exponentially rapidly with $T$ below the critical
temperature in {\em all} the superconducting samples, implying that this
behavior is a {\em signature} of high-$T_c$ superconductivity. The plasma
frequency decreases with increasing Pr content, providing evidence that Pr
depletes carriers, leaving the CuO planes {\em underdoped}. Both the
conductivity in the THz region and the dc resistivity yield evidence for the
opening of a spin gap {\em above} $T_c$.
