Time-frequency (T-F) analysis of signals propagated in dispersive environments or systems is a challenging problem. When considering dispersive waveguides, propagation can be described by modal theory. Propagated signals are usually multicomponent, and the group delay of each mode (i.e., each component) is nonlinear and varies with the mode number. Consequently, existing T-F representations (TFRs) covariant to group delay shifts (GDSs) are not naturally adapted to this context. To overcome this issue, one solution is to approximate the propagation using simple models for which the dispersion properties do not vary with the mode number. If the chosen model is both simple and robust to uncertainties about the waveguide, it can be used to define adapted TFRs, such as the power-class with a suitable power coefficient. This article focuses on a context where this methodology can be applied: low-frequency acoustic propagation in shallow water. In this case, the global oceanic dispersion can be summarized using a single scalar "beta" called the waveguide invariant. This parameter can be used to approximate the group delay of each mode with a power law. Consequently, it is possible to use power-class TFRs with a "beta"-based power coefficient. Their practical use is demonstrated on two experimental data sets: a man-made implosion used for underwater geoacoustic inversion, and a right-whale impulsive vocalization that can be used to localize the animal.