Physics307L F08:People/McCoy/Speed of Light/Word

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Image:Image001_Chad Speed Light.jpg Image:Image002_Chad Speed Light.jpg

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

    1.72 1.92 1.94 1.76

    1.60 2.08 1.64 2.04

    1.36 1.76 1.32 1.76

    1.12 1.56 1.92 1.88

    1.64 2.00 1.44 1.52

    1.16 1.72 1.84 1.80

    1.12 1.56 2.20 2.00

    1.48 1.72 1.56 1.92

    1.64 1.60 1.88 1.64

    1.28 1.44 1.52 1.76

    1.48 1.36 2.08 1.96

    .960 1.72 2.16 1.88

    .800 1.96 1.64 1.84

    1.24 1.48 1.92 1.72

    1.40 1.76 1.76 2.08

    1.42 1.44 1.60 2.16];

calibration_average=mean(calibration_voltage)

calibration_deviation=std(calibration_voltage)

 

test_voltage=[.860 1.06 1.32 1.60 1.48

    1.18 1.02 1.30 1.32 1.60

    .940 1.12 1.00 1.02 1.60

    1.08 1.60 1.68 1.52 1.28

    .940 .780 1.32 1.12 1.52

    1.04 1.34 1.22 1.30 1.92

    .840 1.28 1.40 1.60 1.32

    .820 1.14 1.56 1.48 1.46

    .900 .920 1.44 1.56 1.24

    1.10 1.08 1.40 1.30 2.06

    1.36 1.42 1.48 1.36 1.28

    .880 1.28 1.10 1.48 1.56

    1.28 1.06 1.10 1.22 1.74

    .920 1.32 1.60 1.50 1.38

    .840 1.58 1.34 1.58 1.64

    1.36 1.08 1.46 1.56 1.82

    .760 .840 1.26 1.38 1.38

    1.00 .860 1.40 1.66 1.34

    1.22 1.14 1.50 1.62 1.58

    1.24 1.34 1.22 .980 1.38];

test_average=mean(test_voltage)

test_deviation=std(test_voltage)

 

 

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

 

 

 

Determination of Voltage difference for known Time delay

t_delay=[0 .5 1 2];

calibration_fit=polyfit(t_delay,calibration_average,1)

t_cal_fit=linspace(0,2,100);

v_cal_fit=polyval(calibration_fit,t_cal_fit);

figure

plot(t_delay,calibration_average,'ro',t_cal_fit,v_cal_fit,'k');

xlabel('t(ns)'),ylabel('voltage'),title('Voltage vs. Time delay');

 

 

calibration_fit =

 

    0.2323    1.4852

 

 

 

 

Calculation of Voltage difference for set length difference

x_difference=[0.00,.25,.50,.75,1.00];

length_fit=polyfit(x_difference,test_average,1)

x_fit=linspace(0,1,100);

v_test_fit=polyval(length_fit,x_fit);

figure

plot(x_difference,test_average,'ro',x_fit,v_test_fit,'k');

xlabel('x(m)'),ylabel('voltage'),title('Voltage vs. Difference in length');

 

 

length_fit =

 

    0.4988    1.0472

 

 

 

 

Calculation of Speed of Light from voltage/time relationship and

voltage/length relationship

 

c_mpns=calibration_fit(1)/length_fit(1) %the units of the calibration

%fit are volts/nanosecond, and those of the length fit are volts/meter

c=c_mpns*1e9

 

 

c_mpns =

 

    0.4658

 

 

c =

 

  4.6580e+008

 

 

 

Calculation of minimum and maximum values using error in oscilloscope

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 -> L=minimum, T=maximum

 

t_scope_min(1:2)=calibration_average(1:2)+.02;

t_scope_min(3:4)=calibration_average(3:4)-.02;

V_t_min=polyfit(t_delay,t_scope_min,1)

L_scope_max(1:2)=test_average(1:2)-.02;

L_scope_max(3)=test_average(3);

L_scope_max(4:5)=test_average(4:5)+.02;

V_L_max=polyfit(x_difference,L_scope_max,1)

c_scope_min=abs(V_t_min(1)/V_L_max(1)*1e9)

 

% maximum

% L/T = maximum -> L=maximum, T=minimum

t_scope_max(1:2)=calibration_average(1:2)-.02;

t_scope_max(3:4)=calibration_average(3:4)+.02;

V_t_max=polyfit(t_delay,t_scope_max,1)

L_scope_min(1:2)=test_average(1:2)+.02;

L_scope_min(3)=test_average(3);

L_scope_min(4:5)=test_average(4:5)-.02;

V_L_min=polyfit(x_difference,L_scope_min,1)

c_scope_max=abs(V_t_max(1)/V_L_min(1)*1e9)

 

 

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

 

 

 

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

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 -> L=minimum, T=maximum

 

t_sd_min(1:2)=calibration_average(1:2)+calibration_deviation(1:2);

t_sd_min(3:4)=calibration_average(3:4)-calibration_deviation(3:4);

V_tsd_min=polyfit(t_delay,t_sd_min,1)

L_sd_max(1:2)=test_average(1:2)-test_deviation(1:2);

L_sd_max(3)=test_average(3);

L_sd_max(4:5)=test_average(4:5)+test_deviation(4:5);

V_Lsd_max=polyfit(x_difference,L_sd_max,1)

c_sd_min=abs(V_tsd_min(1)/V_Lsd_max(1)*1e9)

 

% maximum

% L/T = maximum -> L=maximum, T=minimum

t_sd_max(1:2)=calibration_average(1:2)-calibration_deviation(1:2);

t_sd_max(3:4)=calibration_average(3:4)+calibration_deviation(3:4);

V_tsd_max=polyfit(t_delay,t_sd_max,1)

L_sd_min(1:2)=test_average(1:2)+test_deviation(1:2);

L_sd_min(3)=test_average(3);

L_sd_min(4:5)=test_average(4:5)-test_deviation(4:5);

V_Lsd_min=polyfit(x_difference,L_sd_min,1)

c_sd_max=abs(V_tsd_max(1)/V_Lsd_min(1)*1e9)

 

 

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

 

 

 

 

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