Many complex media of great practical interest, such as in medical ultrasound, display an attenuation that increases with a power law as a function of frequency. Usually, measurements can only be taken over a limited frequency range, while wave equations often model attenuation over all frequencies. There is therefore some freedom in how the models behave outside of this limited interval, and many different wave equations have been proposed, in particular, fractional ones. In addition, it is desirable that a wave equation models physically viable media and for that two conditions have to be satisfied. The first is causality, and the second is a criterion that comes from thermodynamic considerations and implies that the relaxation modulus is a completely monotonic function. The latter implies that attenuation asymptotically cannot rise faster than frequency raised to the first power. These criteria will be explained and used to evaluate several of the ordinary and fractional wave equations that exist.