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Justin Long edited subsection_Amplitude_of_Gravitional_Waves__.tex
over 8 years ago
Commit id: 9843b28064a089a27335850b5cc901613760e3c2
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diff --git a/subsection_Amplitude_of_Gravitional_Waves__.tex b/subsection_Amplitude_of_Gravitional_Waves__.tex
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--- a/subsection_Amplitude_of_Gravitional_Waves__.tex
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where $F$ represents electromagnetic energy in gauss, $R_{0}$ represents the distance from the EM source in meters, and $T$ is the time allotted for gravitational radiation in years.
Because we know Gertsenshtein's equation yields an amplitude, we can use a Fourier Transform to calculate the frequency of gravitational waves. For a practical reference, we use known EM measurements of an electric clock (Duke Energy, 2013) to calculate the amplitude and frequency of a gravitational wave.
When an electric clock is measured at 0.3048 meters (1 ft), the strength of its EM field is 15.5 gauss. Calculating for $T = 0.00011408$, we find that the amplitude of the gravitational waves of an electric clock are
\begin{equation}
\frac{a(x)}{b} = 8.11596*10^{-20} \sqrt{\frac{\text{Newton} \text{Second}^3} {\text{Kilogram}^2 \text{Meter}}},
\end{equation}
and when applying a Fourier Transform to calculate the frequency of the gravitational waves we get
\begin{equation}
\int_{-\infty}^{\infty} \frac{a(x)}{b} e^{- 2\pi i x \xi} dx = 7.59863*10^{-18} \sqrt{Hz},
\end{equation}
[put calculations here]