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Chris Spencer edited Data analysis 7.tex
about 10 years ago
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To predict a value of c, the various parameters of the air on the day of measuring are important. c depends on specific heat at constant pressure and volume. Define $X$ as the fraction of air that is water. $X=humidity*\frac{saturated vapor pressure}{barometric pressure}=1.38\%$. Molecular weight is found to be $M_W=0.02880$. Note that $C_p=C_v+R$,where $C_v$ is the heat capacity of wet air. Using the specific heat of superheated steam as 1.4405, $C_v=20.8561$. So $C_p=29.1701$, $\gamma=1.3986$. c is then calculated to be, with $c=\sqrt{\frac{\gamma RT}{M}}=345.205 \frac{m}{s}$, within $.05\%$ of the assumed value of 345.\\
Now we can find c given our equation for $f$ and compare to the theoretical value.
\subsection{Cube}
The table below charts out the first few frequencies and their predicted value of the speed of sound. No errors exceed over
a$1\%$, $1\%$, indicating that the experiment and theory are good approximations.