Deep‐water sound transmission from a moving source to a fixed receiver is studied, where the source emits a random broadband signal whose expected distribution is normal. A bilinear sound‐speed profile is employed, the source is located above the SOFAR axis, and the receiver below. Long ranges are assumed, so that only SOFAR rays need be considered. Basic propagation equations are given, and travel time and spreading loss expressions are approximated in stability regions within which all four SOFAR rays exist for each number of SOFAR‐axis crossings. General equations are derived for the received average power spectrum and power in terms of the spectrum at the source. Then, the broadband signal is taken to be bandlimited white noise. The received spectrum is simplified and examined for nonmultipath, multipath, and Doppler contributions. The influences of range, source speed, frequency, and observation time are considered. Average power at the receiver is studied similarly. Received spectra for a stationary source are investigated, and exhibit greater variations than those arising from a moving source. However, received average power for stationary and moving broadband sources are about equal. Average received power from cw and broadband sources, both moving and stationary, are compared. Power variations in the cw case are found to be much larger than in the broadband case.