So the answer is no. But I don't think you understand why I thought the answer might be yes.
tell me: why should speed have anything to do with wave length ?
it's almost like saying that the vibration on your steering wheel determines the speed of your car
About the car. Let x represent the horizontal velocity and y vertical velocity. Say x is 60 (mph). Then most of the car has vertical velocity 0, so the total velocity is sqrt(60^2 + 0^2) = 60.
Now about the steering wheel. If it's vibrating up and down, at some points its vertical velocity will be some non-zero number y. The total velocity of the steering wheel is sqrt(60^2 + y^2) > 60 while it is moving up and down.
With a beam of light, its horizontal speed in a vacuum is c, right?
But if light has a wavelength and bobs up and down, it also has a non-zero vertical velocity y. The total speed is sqrt(c^2 + y^2) > c, which is a problem.
I'd figure that a photon must travel at a speed less than c horizontally so its total speed remains c. For shorter wavelengths the photon moves faster up and down and thus must move slower horizontally so its total speed is c.
So how is this wrong?