Free space Wavelength

Since free space has a relative permittivity and permeability of one, the wavelength is the longest in free space.

But if the wave propagate in a waveguid, the material in the wave is air and also with the relative permittivity and permeability of one, but the wavelength is not identical with the free-space wavelength.
The wavelength presents the field space distribution on the propagation direction, and can be calculated from the EM field functions(the solution of Maxwell equations with some propagation media, boundary condition and exciter). So the wavelength depends on not only the propagation media, but also the boundary condition and mode. Any complements?

In a waveguide the energy travel at the same speed
than the air as you said but bounce back and forth
from the walls so the net speed is lower