I think the frequency of the wave has no effect whatsoever on the wave speed. The speed of a wave completely depends on the characteristics of the medium it's traveling through.
Physical properties of the medium determine the speed of mechanical waves, like sound, ocean waves, seismic waves, Slinky waves etc. If it depended on the frequency of the waves, then the sound of the band or orchestra would be all smeared out when it reaches you ... you'd hear the drums and bass first, and the flutes and trumpets last.
Electrical properties of the medium determine the speed of electromagnetic waves, like radio, light, and X-rays. If it depended on the frequency of the waves, then you couldn't watch a football game in the stadium or on TV. The reds, oranges, and yellows would reach your eyes first, and then the greens, blues, and violets would arrive later. The action would be all smeared out, and things that happened first might reach your eyes last. What a mess !