Hi,
I was interested in LIGO today as apparently there is big news coming out soon, and was thinking about the detection frequency of gravity waves, apparently LIGO can detect up to 7kHz gravity waves as the max frequency. Since the detection arms are 2km long, and assuming the gravity waves are at the speed of light, then this frequency is just a partial half-wavelength of the gravity wave.
I was wondering if it is theoretically possible to even detect a gravity wave frequency with this interferometer technique (or another technique) if there are multiple wave periods in the detection arm, ie a ~0.4km wavelength, something like 700kHz gravity waves (if travelling at the speed of light).
If gravity waves are stretching the space fabric at a period of 0.4km, with a 2km detection arm, then that is about 5 stretch/shrink periods, so possibly the overall path that light is traveling is the same for a sinusoidal gravity wave perhaps, so an interferometer couldn't detect any gravity waves directly this way maybe.
The other way to look at it is the interferometer light will travel a longer distance on both the positive and and negative portions of the sine wave. If that occurred then I think gravity would not be stretching/shrinking space, but instead would be stretching space in two different directions. If that was true then the interferometer should be able to detect high frequency gravity waves as currently configured, so I am guessing that theory is incorrect :D
So most likely interferometers that have longer arm lengths (ie future space based ones) will have really low frequency response of gravity waves, if the sinusoidal waves cancel out length changes within the interferometer so is there another method I am missing that could be used to detect higher frequency gravity waves with interferometers?
cheers, Jamie