This is the first article in a series of two dealing with the statistical moments of ultrasonic waves transmitted through a disordered medium with resonant multiple scattering. Only the first-order moment is considered here. An ultrasonic pulsed wave is transmitted from a point source to a 128-element receiving array through two-dimensional samples with various thicknesses. The samples consist of random collections of parallel steel rods immersed in water. Experimental results show that the ensemble-averaged transmitted wave forms ("coherent wave") exhibit a time-dependent frequency spectrum. Within the independent scattering approximation, this is well explained by individual resonances of the scatterers. The coherent wave only appears after ensemble averaging and has to be distinguished from the "ballistic wave," i.e., the first well-defined pulse that crosses the sample, which can be measured on every realization of disorder. A physical interpretation is given, which is based on the separation of the coherent wave between a rigid and a resonant contribution.