Could anyone please help me with dimensional analysis

Oct 2016
8
2
http://cdsads.u-strasbg.fr/cgi-bin/nph-iarticle_query?1990ApJ...362..584M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

equation no. 2b is used to calculate acceleration of particles. I am trying to solve it in hypothetical situation and want to know if following parameters taken are correct. (I am looking to get particle acceleration in meters per second)

Unperturbed velocity: some basic assumption in meters per second
Larmor frequency:In angular frequency s
Wave frequency: In angular frequency s
X3 : assumed random number since it is a position along a coordinate axis.
c= speed of light in meters per second
t= time taken for gravity waves to reach particles

Now since α and a are dimensionless, what should I take them as for calculation?
 
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Aug 2010
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174
As far as "dimensional analysis" is concerned, since \(\displaystyle \alpha\) and a are "dimensionless" they can be ignored.
 
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Oct 2016
8
2
As far as "dimensional analysis" is concerned, since \(\displaystyle \alpha\) and a are "dimensionless" they can be ignored.
ok. but if I actually was looking for answer in hypothetical situation wouldnt the amplitude and i (I think is for intensity of wave) would be required?
 

ChipB

PHF Helper
Jun 2010
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Morristown, NJ USA
Your link is not working, so it's difficult to provide any help. But the dimension of frequency is s^-1, not s. Not sure what you mean by \(\displaystyle \alpha\) and 'a' - if \(\displaystyle \alpha\) is radial acceleration then its units are s^-2, and if 'a' means linear acceleration its units are m/s^2.
 
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topsquark

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Apr 2008
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On the dance floor, baby!
http://cdsads.u-strasbg.fr/cgi-bin/nph-iarticle_query?1990ApJ...362..584M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

equation no. 2b is used to calculate acceleration of particles. I am trying to solve it in hypothetical situation and want to know if following parameters taken are correct. (I am looking to get particle acceleration in meters per second)

Unperturbed velocity: some basic assumption in meters per second
Larmor frequency:In angular frequency s
Wave frequency: In angular frequency s
X3 : assumed random number since it is a position along a coordinate axis.
c= speed of light in meters per second
t= time taken for gravity waves to reach particles

Now since α and a are dimensionless, what should I take them as for calculation?
I'm not going to analyze the equations, though there are a number of small errors, like missing brackets. However I can answer your dimensional problems.

As ChipB has stated angular frequencies are measured in Hz = 1/s, \(\displaystyle x^3\) is indeed a coordinate and therefore is measured in m, c is in m/s, and t is (obviously) in s.

\(\displaystyle \alpha\) appears here as a phase shift so it has units of rad. And, as you stated, a is unitless.

The paper doesn't really explain what a might represent. It is clearly not an acceleration. The paper is using a perturbative method...is it possible that a is a variation parameter?

-Dan
 
Oct 2016
8
2
I'm not going to analyze the equations, though there are a number of small errors, like missing brackets. However I can answer your dimensional problems.

As ChipB has stated angular frequencies are measured in Hz = 1/s, \(\displaystyle x^3\) is indeed a coordinate and therefore is measured in m, c is in m/s, and t is (obviously) in s.

\(\displaystyle \alpha\) appears here as a phase shift so it has units of rad. And, as you stated, a is unitless.

The paper doesn't really explain what a might represent. It is clearly not an acceleration. The paper is using a perturbative method...is it possible that a is a variation parameter?

-Dan
So if α is in radian is there any way to calculate radian of gravity waves.Also could amplitude be in decibels? Yes, even I think a is a variation parameter and might be taken in m/s
 
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ChipB

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Jun 2010
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Morristown, NJ USA
Now that I can see the paper, 'a' appears to be dimensionless even though it is described as "amplitude." If 'a' is in decibels it must be based on some fundamental value, which is not given. I think you'd have to look up the paper cited that these equations come from to fully understand just what 'a' is. As for calculating alpha - obviously you would need all the other values in order to do so.
 
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Oct 2016
8
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Now that I can see the paper, 'a' appears to be dimensionless even though it is described as "amplitude." If 'a' is in decibels it must be based on some fundamental value, which is not given. I think you'd have to look up the paper cited that these equations come from to fully understand just what 'a' is. As for calculating alpha - obviously you would need all the other values in order to do so.
@ChipB & @topsquark

I have researched some more and found the paper they mention : http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1981ApJ...248..783P&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf

Even the paper mentioned does not give much about parameters. Also could alpha actually be attenuation constant in decibels?
 
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