Physics307L:People/McCoy/Speed of Light/Word



 



Raw Data and calculations of mean and standard deviation......................................................... 1

Determination of Voltage difference for known Time delay........................................................ 3

Calculation of Voltage difference for set length difference.......................................................... 4

Calculation of Speed of Light from voltage/time relationship and................................................ 5

Calculation of minimum and maximum values using error in oscilloscope.................................. 6

Calculation of minimum and maximum values within 1 standard deviation of mean................... 7



Raw Data and calculations of mean and standard deviation

calibration_voltage=[1.84 2.24 2.36 2.20

    .960 1.44 1.84 2.24

    2.08 1.52 1.88 1.48

    1.28 1.36 1.68 2.04

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p class=M-code>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

<p class=MsoNormal>

calibration_average =

1.3790    1.6820    1.8090    1.8840

calibration_deviation =

0.3192    0.2521    0.2663    0.2112

test_average =

1.0280    1.1630    1.3550    1.4080    1.5290

test_deviation =

0.1888    0.2301    0.1741    0.2020    0.2237

<p class=MsoNormal>

Determination of Voltage difference for known Time delay</a>

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

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

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

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

<p class=M-code>figure

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

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

<p class=MsoNormal>

calibration_fit =

0.2323    1.4852

<p class=MsoNormal>

<p class=MsoNormal>

Calculation of Voltage difference for set length difference</a>

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

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

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

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

<p class=M-code>figure

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

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

<p class=MsoNormal>

length_fit =

0.4988    1.0472

<p class=MsoNormal>

<p class=MsoNormal>

Calculation of Speed of Light from voltage/time relationship and</a>

<p class=MsoNormal>voltage/length relationship

<p class=MsoNormal>

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

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

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

<p class=MsoNormal>

c_mpns =

0.4658

c =

4.6580e+008

<p class=MsoNormal>

Calculation of minimum and maximum values using error in oscilloscope</a>

<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 class=MsoNormal>

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

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

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

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

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

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

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

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

<p class=M-code>

<p class=M-code>% maximum

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

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

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

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

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

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

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

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

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

<p class=MsoNormal>

V_t_min =

0.2095    1.5052

V_L_max =

0.5468    1.0232

c_scope_min =

3.8311e+008

V_t_max =

0.2552    1.4652

V_L_min =

0.4508    1.0712

c_scope_max =

5.6610e+008

<p class=MsoNormal>

Calculation of minimum and maximum values within 1 standard deviation of mean</a>

<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 class=MsoNormal>

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

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

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

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

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

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

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

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

<p class=M-code>

<p class=M-code>% maximum

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

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

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

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

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

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

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

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

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

<p class=MsoNormal>

V_tsd_min =

-0.0624    1.7665

V_Lsd_max =

1.0016    0.7972

c_sd_min =

6.2296e+007

V_tsd_max =

0.5271    1.2039

V_Lsd_min =

-0.0040    1.2972

c_sd_max =

1.3084e+011

<p class=MsoNormal>

<p class=MsoNormal>