We present a numerical analysis of the gravitational radiation due to the radial infall of a particle into a Schwarzschild black hole starting at infnity with no initial velocity. We compute the radiated waveforms, spectra and energies for multipoles up to l = 6, improving signicantly on the numerical accuracy of existing results. The wave exhibits a "ring-down" phase whose dominant contribution is a superposition of the quasi-normal modes of the black hole. The numerical accuracy allows us to recover the frequencies of these modes through a fit of that part of the wave. Comparing with direct computations of the quasi-normal modes we reach a ~10-4 to ~10-2 accuracy for the first two overtones of each multipole. Our numerical accuracy also allows us to display the power-law tail that the wave develops after the ring-down has been exponentially cut-off. The amplitude of this contribution is ~102 to ~103 times smaller than the typical scale of the wave.