# Relationship between the dimension of a chip and its operation frequency

In his book "Modern Operating Systems", Tanenbaum makes a statement about processors speed that I can't understand:

According to Einstein’s special theory of relativity, no electrical signal can propagate faster than the speed of light, which is about 30 cm/nsec in vacuum and about 20 cm/nsec in copper wire or optical fiber. This means that in a computer with a 10-GHz clock, the signals cannot travel more than 2 cm in total. For a 100-GHz computer the total path length is at most 2 mm. A 1-THz (1000-GHz) computer will have to be smaller than 100 microns, just to let the signal get from one end to the other and back once within a single clock cycle.

I am aware that the speed of an electromagnetial perturbation is not the same in different environments, so it is easy to grasp that the speed of light "is about 30 cm/nsec in vacuum and about 20 cm/nsec in copper wire or optical fiber". However, how it is possible to infer that signals traveling inside a 10-GHz CPU cannot travel more than 2 cm? Is that related somehow to the wavelength of a 10 GHz signal that is traveling at 20 cm/nsec? If it is related, how to conclude that an 1-THz CPU would have to be smaller than 100 microns, once the wavelength of an 1-THz signal is 200 microns?

• They can travel more than 2cm, but it will take more than 1 clock cycle for them to do so – BeB00 Nov 10 '17 at 18:15