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

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The discussion focuses on the impact of gravitational waves (GW) on a 1-foot steel bar when subjected to high frequencies ranging from 1 MHz to 100 MHz. It concludes that the response speed of inter-atomic forces in steel, approximately 20,000 feet per second, is significantly slower than the frequencies of the GWs, leading to negligible length changes in the bar. The expected length change is estimated to be 6 to 9 orders of magnitude smaller than the metric deviation caused by the GW. Consequently, the bar's atoms will move along geodesics, resulting in minimal interaction with the GW.

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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.
 
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Paul Colby said:
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.

Paul Colby said:
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.
 
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PeterDonis said:
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.
 

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