Beginning with the normal mode expansion for the acoustic field at a fixed receiver due to a source that moves at constant depth on a straight‐line course (not necessarily a radial from the receiver) [K. E. Hawker, J. Acoust. Soc. Am.65, 675–681 (1979)] while emitting a time‐harmonic signal, an expression is derived for the correlations among the modal components of the field generated by such a source whose emission is a statistically stationary random process with nonzero bandwidth. This expression is used to identify the degradation suffered by the modal components of the received signal autocorrelation due to experimental time integration. An illustrative example of a low‐frequency narrow‐band source in a shallow water environment is examined. There, the motion of the source results in Doppler splitting of the single source emission line into a group of modal spectral lines at the receiver. Recently it has been experimentally verified [Glattetreetal., J. Acoust. Soc. Am.86, 680–690 (1989)] that for a ‘‘collision course’’ (one that passes directly over the receiver) these lines are stable, resolvable features of the received spectrum. The source in the example, however, is on a ‘‘near miss’’ heading that passes the receiver at a range of 2 km. This produces a time dependence in the frequencies of the Doppler lines that makes their experimental resolution problematic. It is concluded, however, that some of the structure of this line group should still be experimentally resolvable.