The effects of internal waves on low-frequency (25-Hz) wide-band source localization performance are investigated at a very long range (1000 km). Sound-speed perturbations induced by internal waves obeying the Garrett-Munk spectral model are incorporated into the normal mode solution to the wave equation using the adiabatic approximation. Source range estimates are limited by very random internal waves and do not improve with increasing SNR. In an attempt to combat this limitation due to environmental uncertainty, processors can benefit from the spectrum of the acoustic source. According to the hybrid Cramer-Rao lower bound (CRLB), significant improvements on range estimates are possible when using a coherent wide-band acoustic source with bandwidth of 10 Hz on the 25-Hz source. The CRLB provides valuable analytical insight into the limits on source range estimates, but the optimal signal processing algorithm is necessary to compute the actual limits on source localization. Using a coherent wide-band source with many discrete frequencies spanning the bandwidth, significant gains in range estimates are achieved by optimally incorporating this signal spectrum into the localization algorithm a priori.