How does LIGO detect accurate time differences if gravitational waves are also compressing and stretching the light waves-specific confusion below

Question

I was watching this veritaserum which explains my question at 5:55 https://www.youtube.com/watch?v=iphcyNWFD10 saying that the speed of light is much faster so will pass through the arms multiple times during each compression/stretch and the changingintensity of light in the interference pattern overtime can be detected but I thought gravitational waves travelled at the speed of light?

Answer 1

What he's referring to is the time it takes light to travel down and back vs. the period $T$ of the gravitational wave. There is no theoretical limit on $T$.

Gravity waves do travel at $c$.

Answer 2

Gravity propagates at light speed but the masses moving to create the gravitational waves are moving below light speed. The frequency of the gravitational wave will correspond to the rotation or orbits of the moving bodies creating it.