Wave phenomena involve perturbations whose behavior is equivalent in space and time. The perturbations may be of very different nature but they all have to conform with the notion of a field, that is, a scalar or vector quantity defined for all points in space. Some wave phenomena are described in terms of only one field. For example water waves where the perturbation is the level above or below from the equilibrium position. Nonetheless, electromagnetic waves require the existence of two fields. I shall argue that in fact, all wave phenomena involve two fields although we sometimes perform the description in terms of only one field.
To this end, the concept of cyclic or dynamical equilibrium will be put forward where the system continuously moves between two states where it exchanges two forms of energy. In a mechanical system it may be, for example, kinetic and potential energy. Differential equations that form an Ermakov pair require the existence of two linearly independent fields. These equations possess an invariant. For the time dependent harmonic oscillator, such an invariant exists only for time dependent potentials that are physically attainable.
According to this view, two fields must be present in any physical system that exhibits wave behavior. In the case of gravity, if it exhibits wave behavior, there must be a complementary field that also carries energy. It is also interesting that the complex cosmic tension field proposed by Chandrasekar involves a complex field because complex functions formally describe two complementary fields.