Why Inside a coax the dielectric between center conductor and shield slows the wave to a fraction of its free-space speed, described by the velocity factor (about 0.66 for solid polyethylene, 0.78-0.85 for foam, 1.0 for air). Because the wave travels slower, the wavelength inside the cable is shorter, so a given physical piece of cable contains more wavelengths than the same distance in air. That is why, in electrical degrees or wavelengths, the cable measures longer than a tape measure says. To cut a quarter-wave stub you multiply the free-space quarter wavelength by the velocity factor.
Watch out Nothing propagates faster than light in free space, so the choice saying waves move faster in coax is impossible; skin effect relates to conductor loss and current distribution, not to propagation speed.
Slower wave, shorter wavelength, more wavelengths per foot: physical length times VF gives the free-space equivalent.