Physics307L:People/McCoy/Speed of Light/Word

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<div class=Section1>

<p class=MsoToc2>Raw Data and calculations of mean and standard deviation......................................................... 1</p>

<p class=MsoToc2>Determination of Voltage difference for known Time delay........................................................ 3</p>

<p class=MsoToc2>Calculation of Voltage difference for set length difference.......................................................... 4</p>

<p class=MsoToc2>Calculation of Speed of Light from voltage/time relationship and................................................ 5</p>

<p class=MsoToc2>Calculation of minimum and maximum values using error in oscilloscope.................................. 6</p>

<p class=MsoToc2>Calculation of minimum and maximum values within 1 standard deviation of mean................... 7</p>

<p class=MsoNormal>&nbsp;</p>

<h2><a name="_Toc210396835">Raw Data and calculations of mean and standard deviation</a></h2>

<p class=M-code>calibration_voltage=[1.84 2.24 2.36 2.20</p>

<p class=M-code>    .960 1.44 1.84 2.24</p>

<p class=M-code>    2.08 1.52 1.88 1.48</p>

<p class=M-code>    1.28 1.36 1.68 2.04</p>

<p class=M-code>    1.72 1.92 1.94 1.76</p>

<p class=M-code>    1.60 2.08 1.64 2.04</p>

<p class=M-code>    1.36 1.76 1.32 1.76</p>

<p class=M-code>    1.12 1.56 1.92 1.88</p>

<p class=M-code>    1.64 2.00 1.44 1.52</p>

<p class=M-code>    1.16 1.72 1.84 1.80</p>

<p class=M-code>    1.12 1.56 2.20 2.00</p>

<p class=M-code>    1.48 1.72 1.56 1.92</p>

<p class=M-code>    1.64 1.60 1.88 1.64</p>

<p class=M-code>    1.28 1.44 1.52 1.76</p>

<p class=M-code>    1.48 1.36 2.08 1.96</p>

<p class=M-code>    .960 1.72 2.16 1.88</p>

<p class=M-code>    .800 1.96 1.64 1.84</p>

<p class=M-code>    1.24 1.48 1.92 1.72</p>

<p class=M-code>    1.40 1.76 1.76 2.08</p>

<p class=M-code>    1.42 1.44 1.60 2.16];</p>

<p class=M-code>calibration_average=mean(calibration_voltage)</p>

<p class=M-code>calibration_deviation=std(calibration_voltage)</p>

<p class=M-code>&nbsp;</p>

<p class=M-code>test_voltage=[.860 1.06 1.32 1.60 1.48</p>

<p class=M-code>    1.18 1.02 1.30 1.32 1.60</p>

<p class=M-code>    .940 1.12 1.00 1.02 1.60</p>

<p class=M-code>    1.08 1.60 1.68 1.52 1.28</p>

<p class=M-code>    .940 .780 1.32 1.12 1.52</p>

<p class=M-code>    1.04 1.34 1.22 1.30 1.92</p>

<p class=M-code>    .840 1.28 1.40 1.60 1.32</p>

<p class=M-code>    .820 1.14 1.56 1.48 1.46</p>

<p class=M-code>    .900 .920 1.44 1.56 1.24</p>

<p class=M-code>    1.10 1.08 1.40 1.30 2.06</p>

<p class=M-code>    1.36 1.42 1.48 1.36 1.28</p>

<p class=M-code>    .880 1.28 1.10 1.48 1.56</p>

<p class=M-code>    1.28 1.06 1.10 1.22 1.74</p>

<p class=M-code>    .920 1.32 1.60 1.50 1.38</p>

<p class=M-code>    .840 1.58 1.34 1.58 1.64</p>

<p class=M-code>    1.36 1.08 1.46 1.56 1.82</p>

<p class=M-code>    .760 .840 1.26 1.38 1.38</p>

<p class=M-code>    1.00 .860 1.40 1.66 1.34</p>

<p class=M-code>    1.22 1.14 1.50 1.62 1.58</p>

<p class=M-code>    1.24 1.34 1.22 .980 1.38];</p>

<p class=M-code>test_average=mean(test_voltage)</p>

<p class=M-code>test_deviation=std(test_voltage)</p>

<p class=MsoNormal>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>calibration_average =</p>

<p class=output>&nbsp;</p>

<p class=output>    1.3790    1.6820    1.8090    1.8840</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>calibration_deviation =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.3192    0.2521    0.2663    0.2112</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>test_average =</p>

<p class=output>&nbsp;</p>

<p class=output>    1.0280    1.1630    1.3550    1.4080    1.5290</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>test_deviation =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.1888    0.2301    0.1741    0.2020    0.2237</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=MsoNormal>&nbsp;</p>

<h2><a name="_Toc210396836">Determination of Voltage difference for known Time delay</a></h2>

<p class=M-code>t_delay=[0 .5 1 2];</p>

<p class=M-code>calibration_fit=polyfit(t_delay,calibration_average,1)</p>

<p class=M-code>t_cal_fit=linspace(0,2,100);</p>

<p class=M-code>v_cal_fit=polyval(calibration_fit,t_cal_fit);</p>

<p class=M-code>figure</p>

<p class=M-code>plot(t_delay,calibration_average,'ro',t_cal_fit,v_cal_fit,'k');</p>

<p class=M-code>xlabel('t(ns)'),ylabel('voltage'),title('Voltage vs. Time delay');</p>

<p class=MsoNormal>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>calibration_fit =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.2323    1.4852</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=MsoNormal>&nbsp;</p>


<p class=MsoNormal>&nbsp;</p>

<h2><a name="_Toc210396837">Calculation of Voltage difference for set length difference</a></h2>

<p class=M-code>x_difference=[0.00,.25,.50,.75,1.00];</p>

<p class=M-code>length_fit=polyfit(x_difference,test_average,1)</p>

<p class=M-code>x_fit=linspace(0,1,100);</p>

<p class=M-code>v_test_fit=polyval(length_fit,x_fit);</p>

<p class=M-code>figure</p>

<p class=M-code>plot(x_difference,test_average,'ro',x_fit,v_test_fit,'k');</p>

<p class=M-code>xlabel('x(m)'),ylabel('voltage'),title('Voltage vs. Difference in length');</p>

<p class=MsoNormal>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>length_fit =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.4988    1.0472</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=MsoNormal>&nbsp;</p>


<p class=MsoNormal>&nbsp;</p>

<h2><a name="_Toc210396838">Calculation of Speed of Light from voltage/time relationship and</a></h2>

<p class=MsoNormal>voltage/length relationship</p>

<p class=MsoNormal>&nbsp;</p>

<p class=M-code>c_mpns=calibration_fit(1)/length_fit(1) %the units of the calibration</p>

<p class=M-code>%fit are volts/nanosecond, and those of the length fit are volts/meter</p>

<p class=M-code>c=c_mpns*1e9</p>

<p class=MsoNormal>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>c_mpns =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.4658</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>c =</p>

<p class=output>&nbsp;</p>

<p class=output>  4.6580e+008</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=MsoNormal>&nbsp;</p>

<h2><a name="_Toc210396839">Calculation of minimum and maximum values using error in oscilloscope</a></h2>

<p class=MsoNormal>Margin of error in oscilloscope calculations = .02V Minimum slope would be found with maximum value(n+.02) for data less than median and minimum value (n-.02) for data greater than median minimum L/T = minimum -&gt; L=minimum, T=maximum</p>

<p class=MsoNormal>&nbsp;</p>

<p class=M-code>t_scope_min(1:2)=calibration_average(1:2)+.02;</p>

<p class=M-code>t_scope_min(3:4)=calibration_average(3:4)-.02;</p>

<p class=M-code>V_t_min=polyfit(t_delay,t_scope_min,1)</p>

<p class=M-code>L_scope_max(1:2)=test_average(1:2)-.02;</p>

<p class=M-code>L_scope_max(3)=test_average(3);</p>

<p class=M-code>L_scope_max(4:5)=test_average(4:5)+.02;</p>

<p class=M-code>V_L_max=polyfit(x_difference,L_scope_max,1)</p>

<p class=M-code>c_scope_min=abs(V_t_min(1)/V_L_max(1)*1e9)</p>

<p class=M-code>&nbsp;</p>

<p class=M-code>% maximum</p>

<p class=M-code>% L/T = maximum -&gt; L=maximum, T=minimum</p>

<p class=M-code>t_scope_max(1:2)=calibration_average(1:2)-.02;</p>

<p class=M-code>t_scope_max(3:4)=calibration_average(3:4)+.02;</p>

<p class=M-code>V_t_max=polyfit(t_delay,t_scope_max,1)</p>

<p class=M-code>L_scope_min(1:2)=test_average(1:2)+.02;</p>

<p class=M-code>L_scope_min(3)=test_average(3);</p>

<p class=M-code>L_scope_min(4:5)=test_average(4:5)-.02;</p>

<p class=M-code>V_L_min=polyfit(x_difference,L_scope_min,1)</p>

<p class=M-code>c_scope_max=abs(V_t_max(1)/V_L_min(1)*1e9)</p>

<p class=MsoNormal>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_t_min =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.2095    1.5052</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_L_max =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.5468    1.0232</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>c_scope_min =</p>

<p class=output>&nbsp;</p>

<p class=output>  3.8311e+008</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_t_max =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.2552    1.4652</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_L_min =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.4508    1.0712</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>c_scope_max =</p>

<p class=output>&nbsp;</p>

<p class=output>  5.6610e+008</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=MsoNormal>&nbsp;</p>

<h2><a name="_Toc210396840">Calculation of minimum and maximum values within 1 standard deviation of mean</a></h2>

<p class=MsoNormal>Margin of error = 1 standard deviation Minimum slope would be found with maximum value(n+sd) for data less than median and minimum value (n-sd) for data greater than median minimum L/T = minimum -&gt; L=minimum, T=maximum</p>

<p class=MsoNormal>&nbsp;</p>

<p class=M-code>t_sd_min(1:2)=calibration_average(1:2)+calibration_deviation(1:2);</p>

<p class=M-code>t_sd_min(3:4)=calibration_average(3:4)-calibration_deviation(3:4);</p>

<p class=M-code>V_tsd_min=polyfit(t_delay,t_sd_min,1)</p>

<p class=M-code>L_sd_max(1:2)=test_average(1:2)-test_deviation(1:2);</p>

<p class=M-code>L_sd_max(3)=test_average(3);</p>

<p class=M-code>L_sd_max(4:5)=test_average(4:5)+test_deviation(4:5);</p>

<p class=M-code>V_Lsd_max=polyfit(x_difference,L_sd_max,1)</p>

<p class=M-code>c_sd_min=abs(V_tsd_min(1)/V_Lsd_max(1)*1e9)</p>

<p class=M-code>&nbsp;</p>

<p class=M-code>% maximum</p>

<p class=M-code>% L/T = maximum -&gt; L=maximum, T=minimum</p>

<p class=M-code>t_sd_max(1:2)=calibration_average(1:2)-calibration_deviation(1:2);</p>

<p class=M-code>t_sd_max(3:4)=calibration_average(3:4)+calibration_deviation(3:4);</p>

<p class=M-code>V_tsd_max=polyfit(t_delay,t_sd_max,1)</p>

<p class=M-code>L_sd_min(1:2)=test_average(1:2)+test_deviation(1:2);</p>

<p class=M-code>L_sd_min(3)=test_average(3);</p>

<p class=M-code>L_sd_min(4:5)=test_average(4:5)-test_deviation(4:5);</p>

<p class=M-code>V_Lsd_min=polyfit(x_difference,L_sd_min,1)</p>

<p class=M-code>c_sd_max=abs(V_tsd_max(1)/V_Lsd_min(1)*1e9)</p>

<p class=MsoNormal>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_tsd_min =</p>

<p class=output>&nbsp;</p>

<p class=output>   -0.0624    1.7665</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_Lsd_max =</p>

<p class=output>&nbsp;</p>

<p class=output>    1.0016    0.7972</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>c_sd_min =</p>

<p class=output>&nbsp;</p>

<p class=output>  6.2296e+007</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_tsd_max =</p>

<p class=output>&nbsp;</p>

<p class=output>    0.5271    1.2039</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>V_Lsd_min =</p>

<p class=output>&nbsp;</p>

<p class=output>   -0.0040    1.2972</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=output>c_sd_max =</p>

<p class=output>&nbsp;</p>

<p class=output>  1.3084e+011</p>

<p class=output>&nbsp;</p>

<p class=output>&nbsp;</p>

<p class=MsoNormal>&nbsp;</p>

<p class=MsoNormal>&nbsp;</p>

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