Gravitational waves: effect of frequency on strain

[RyuuJin]

Hi guys. I am having a little trouble understanding a few relations professor mentioned at lectures, regarding gravitational waves - flux of energy and strain.

First one expresses how is the flux of energy F related to frequency of radiation f and inflicted strain h. And the second one is for strain.

I can't quite understand, why would flux (or strain) decrease with frequency? Shouldn't strain get higher (e.g. inspiral of black holes)??

Thanks!

 

[stefan r]

Hi guys. I am having a little trouble understanding a few relations professor mentioned at lectures, regarding gravitational waves - flux of energy and strain.

First one expresses how is the flux of energy F related to frequency of radiation f and inflicted strain h. And the second one is for strain.

View attachment 200262

I can't quite understand, why would flux (or strain) decrease with frequency? Shouldn't strain get higher (e.g. inspiral of black holes)??

Thanks!

It is increasing with f. f² is positive.

edit, I know almost nothing about gravity waves. Just looking at (f/1kHz). "f" is a frequency. "1/1kHz" makes that a dimensionless term. Your flux has to be in dimensions W/m². A 2 kilohertz radiation frequency would be 2kHz/1kHz = 2. So a source with 2 kilohertz has 4 times the flux as a source with 1 kilohertz.

 

[RyuuJin]

Sorry, I didn't write correctly (I am going to edit now). Actually both my questions are regarding strain. In the first equation, if you want to keep flux constant, than with higher frequency you get lower strain?? Why would that be?

 

[RyuuJin]

Hi guys. I am having a little trouble understanding a few relations professor mentioned at lectures, regarding gravitational waves - flux of energy and strain.

First one expresses how is the flux of energy F related to frequency of radiation f and inflicted strain h. And the second one is for strain.

View attachment 200262

I can't quite understand, why would flux (or strain) decrease with frequency? Shouldn't strain get higher (e.g. inspiral of black holes)??

Thanks!

EDIT: Sorry didn't write the question right: I can't quite understand, why would strain decrease with frequency (if you keep flux constant)? Shouldn't strain get higher (e.g. inspiral of black holes)??

 

[stefan r]

EDIT: Sorry didn't write the question right: I can't quite understand, why would strain decrease with frequency (if you keep flux constant)? Shouldn't strain get higher (e.g. inspiral of black holes)??

A 100 stellar mass black hole binary would increase energy radiation has they spiral in.
-A 2 second orbital period radiates 1/4th the energy of a 1 second orbit.
-A 400 stellar mass black hole binary with 2 second orbital period radiates the same energy as a 100 stellar mass binary with 1 second orbital period.
-A 100 stellar mass black hole binary with 2 second orbital period will have a strain measurement here that is the same as a 100 stellar mass black hole binary with 1 second orbital period which is twice as far away.

Consider a source A a source B. The flux is equal but source A has 10X frequency. So source B must be closer or more massive or some combination. So you could say "source B has higher strain because it has lower frequency". Really source B has higher strain because it is either closer or more massive.