Well if wave speed isn't fixed then all bets are off. Fixed wave speed limits them to an inverse relationship. Without a fixed wave speed there doesn't have to be a relationship between frequency and wavelength, so you could simply increase wavelength with the same frequency to get a higher speed, etc.
I guess you could look at it like that. For two things to be dependent on each other whether directly or inversely, they have to be defined by something else you're holding constant. For instance P1V1 = P2V2 , the PxV relationship there is defined by nRT being held constant.