Experiments have been performed in a two‐layer stably stratified flow where the mean velocity surpasses the phase speed of all internal waves of mode one. Results show the existence of two wave trains propagating in the direction of the mean flow (excited by a two‐dimensional wave maker), which are identified by the modulation of the amplitude of the linearly superposed wave trains. Measurements of the composite wave speed and dispersion relation are presented. Wave speeds are shown to be very near the mean. The qualitative behavior of composite wave trains is shown to appear similar to that of unstable Kelvin–Helmholtz waves where spatial growth is dominant, leading to possible misinterpretation.