Michael Morag edited Data Analysis.tex  about 10 years ago

Commit id: 6effc4595ce9e2f1dc77d7b964932ee9269f9602

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\[\eta=\frac{ck}{\omega}\]  where $\eta$ is index of refraction, $k$ is the wavenumber, and $\omega$ is the angular frequency. Since $k=\frac{2\pi}{\lambda}$ and $\omega=2\pi f$, then index of refraction can be expressed as   \[\eta=\frac{c}{\lambda f}\]  The results can be seen in figures 1 through 4. Wavelengths were found by finding the distance between two maximums or two minimums and then multiplying by the scale factor used when taking the measurement, which changed based on the measured frequency. As it can be seen in figure 1, 2,  the measured index of refraction concurred with the simulated data, confirming the validity of Appleton's equation over the frequency range measured. This method was limited at the low frequency that was used on the plane data, 40 MHz, by the angle at which the wavelength was measured. At angles above 45\textsuperscript{o}, full and even half wavelengths cannot be seen, which is reflected in figure 3. Up until 25\textsuperscript{o}, the measured index of refractions agreed with the theoretical values. Index of refractions of angles larger than 25\textsuperscript{o} led to some incongruities with the largest difference being at 30\textsuperscript{o} with 18\% error from expected value. Larger error margins could have probably come about from wavelengths measured at larger angles where only half of the wavelength was measured and doubled to acquire the full wavelength, potentially having the simulated data be within the error bars.