I Effect of GW on Steel Bars: What's the Impact?

[Paul Colby]

What is the effect of a high frequency, where high is say 1MH to 100MHz on a bar of steel say 1 foot in length? A GW passes at the speed of light with a wavelength much longer than any acoustic response of the bar and well above any resonance. Intuitively (which I don't give much weight in this case) if the metric deviation is say $10^{-27}$ I would expect the length change of the bar to be much smaller (6 to 9) orders of magnitude than the metric deviation.

 

[PeterDonis]

What is the effect of a high frequency, where high is say 1MH to 100MHz on a bar of steel say 1 foot in length?

The key factor will be how fast the forces between the atoms in the bar can compensate for the change in the metric due to the GW. This response speed is basically the speed of sound in the bar. The sound speed in steel is about 20,000 feet per second, which for a 1 foot bar corresponds to a response frequency of about 20 kHz. This is much lower than the GW frequencies you are hypothesizing, so the bar's response will be much too slow to affect how the atoms move.

I would expect the length change of the bar to be much smaller (6 to 9) orders of magnitude than the metric deviation.

I would not, based on the above quick and dirty analysis. Since the inter-atomic forces in the bar are much too slow to keep up with the metric changes induced by the GW, the bar's atoms will basically move on geodesics as far as the GW is concerned, which means the length change of the bar should be of the same order as the metric deviation.

 

[Paul Colby]

I would not, based on the above quick and dirty analysis. Since the inter-atomic forces in the bar are much too slow to keep up with the metric changes induced by the GW, the bar's atoms will basically move on geodesics as far as the GW is concerned, which means the length change of the bar should be of the same order as the metric deviation.

A couple years ago I looked at some radio and optical frequency GW detection schemes. The analysis basically hinges on this view of material motion being the case. Your argument makes sense, thanks.