# Physics307L F08:People/Osinski/Lightspeed/Lightspeed.m

```%% 1st Calibration
delay1=[0 .5 1 2 4 6 8 10];
voltage1=[5.64 5.76 5.88 6.16 6.60 6.84 7.12 7.32];
figure(1)
subplot(2,2,1)
plot(delay1,voltage1),title('1st Calibration'),xlabel('delay (ns)'),ylabel('voltage (V)')
% the actual signal produced by a delay is given by the value subtracted
% from the 0 delay value.
realvolt1=voltage1-voltage1(1);
% I ignore the first 3 elements of my voltage data vector in order to determine
% the proportionality factor between 2ns and the time difference.
Calib1=[realvolt1(4),realvolt1(5)-realvolt1(4),realvolt1(6)-realvolt1(5),...
realvolt1(7)-realvolt1(6),realvolt1(8)-realvolt1(7)];
stdCalib1=std(Calib1)
% Now I find the mean of these values so that I get one number as the
% proportionality factor.
Calib1=mean(Calib1);
% I repeat the same procedure for Calibration 2 and then find their average
%% 2nd Calibration
delay2=[0 .5 1 2 4 6 8 10];
voltage2=[5.00 5.12 5.24 5.44 5.88 6.28 6.64 6.88];
subplot(2,2,2)
plot(delay2,voltage2),title('2nd Calibration'),xlabel('delay (ns)'),ylabel('voltage (V)')
realvolt2=voltage2-voltage2(1);
Calib2=[realvolt2(4),realvolt2(5)-realvolt2(4),realvolt2(6)-realvolt2(5),...
realvolt2(7)-realvolt2(6),realvolt2(8)-realvolt2(7)];
stdCalib2=std(Calib2);
STDCALIB=(stdCalib2+stdCalib1)/2
Calib2=mean(Calib2);
CALIB=(Calib1+Calib2)/2 %this tells me how to read time from the voltage signal on the scope
%% 1st Data Set
D1=0:10:150;
V1=[5.80 5.72 5.64 5.52 5.44 5.40 5.36 5.28 5.28 5.12 4.96 4.96 4.96 4.88 4.64 4.64];
subplot(2,2,3)
plot(D1,V1),title('1st Raw Data Set'),xlabel('distance (cm)'),ylabel('voltage (V)')
%% 2nd Data set
D2=0:10:150;
D2(2)=11;
V2=[5.76 5.68 5.56 5.56 5.52 5.36 5.32 5.28 5.16 5.08 5.00 4.92 4.92 4.80 4.88 4.76];
subplot(2,2,4)
plot(D2,V2),title('2nd Raw Data Set'),xlabel('distance (cm)'),ylabel('voltage (V)')
%% Averaging Data
AVG=(V1+V2)./2;
figure(2)
plot(D1,AVG),title('averaged data'),xlabel('distance (cm)'),ylabel('voltage (V)')
%% Translation from voltage to time to speed
% Both data sets span a distance of 1.5m. I find the total change in
% voltage from begining to end for both sets and then average this
% quantity.
deltaV1=V1(1)-V1(end)
deltaV2=V2(1)-V2(end)
DELTAV=(deltaV1+deltaV2)/2
% In order to convert DELTAV from voltage to time I use the
% proportionality factor, CALIB/2, calculated above (divided by 2 so that I get my answer in terms of ns).
TIME=(2*DELTAV)/CALIB
DISTANCE=1.5
LIGHTSPEED=DISTANCE/TIME
% My result is in m/ns so I make sure to do the proper conversiion later.
%% Standard Deviation of the Mean
% Using the mean value of data calculated I above I subract each data set
% from the mean to obtain the deviation of each data point from the mean.
% Then I find the mean of the squared deviations (variance). Since each
% data point has really only been taken twice the standard deviation is
% going to be the same as the std of the mean since dividing by sqrt(N-1)
% does not make any difference when N is only 2.
Mean1=AVG-V1;
Mean2=AVG-V2;
Var1=(sum(Mean1.^2))/length(Mean1);
Var2=(sum(Mean2.^2))/length(Mean2);
STDmean1=sqrt(Var1);
STDmean2=sqrt(Var2);
STDMEAN=(STDmean1+STDmean2)/2```