Help Needed with Franck Hertz Oscillation Lab Report Analysis

[jenny777]

Hello,

I'm writing my lab report for my Franck Hertz oscillation and I seem to be stuck on analysis part where I have to perform auto-correlations.

Could anyone please guide me through steps 2-4 on excel? I absolute have no idea what the steps 2-4 is asking me to do. For instance, for step 2 I don't understand how i can get a least squares fir for my maxima and minima only. I really appreciate any sort of help

I've included a picture of my graph

Step 2:

Do a least squares fit to the data (location of maxima and minima), and record the values
of the slope and intercept and their uncertainties. (Note that the zero point may not be zero
because of an offset voltage in the data, the contact potential). You may have time to do this
before you leave the lab, as well.

Step 3:

Subtract the value of the best-fit line from your original data. Provide a graph containing
the values before and after subtraction.

Step 4:

Perform an auto-correlation for 10 delays centered on the voltage nearest the wavelength
estimate derived above. Record these values and plot them on a graph. Show intermediate work
for at least one non-zero delay calculation.

 

[voko]

The minima or maxima must be all on a straight line. So the function of the current vs voltage must be $I = I_0 + c(V - V_0)$, where $I_0$, $c$ and $V_0$ are to be determined from the experimental data (one set for minima, another for maxima). This is done by the least squares fit.

 

[jenny777]

First of all, thank you so much for replying, but what is the "c" in this equation?
I've determined the max to be 14.2081, 19.6054, 24.4002. and min are 17.4066, 22.2012, 27.3981. So does my straight line have to include all those points?

And also, why doesn't my graph look like the ones likes the picture below? (I've included the pic from wikipedia). When I flip the currents from negative to positive values, the max and min points also change.

Should I flip the currents? or no...

Thank you

 

[voko]

$I_0$, $V_0$ and $c$ are what you are supposed to find using the least squares method. Are you familiar with the method?

 

[jenny777]

hmm... yes I'm familiar with the method of least squares fit. but what exactly am I looking for here?
What I did is that, I plotted the accelerating voltage vs. order of peaks, and applied linear regression. my slope for maxima was 5.0 and for minima I got 4.99. Am I on the right track?

 

[jenny777]

graphs

here's my graphs

 

[jenny777]

And can you please let me know how to do an auto-correlation for 10 delays? I have never dealt with auto-correlations in my life. and i haven't got a clue how to do so

 

[voko]

I am not sure what you mean by the "order of peaks".

I have re-read the entire assignment and it appears that they want you to produce a single best-fit line, using least squares, based on the values at maxima and minima.

The next step is to subtract the best-fit line from the original data. Then I believe they want you to do auto-correlation on the result.

 

[jenny777]

Auto-correlation

So the first graph is the original curve, and the second graph is the auto-correlated graph. Does this make sense?

What I did was, I did quadratic regression on my original curve and called it f(x). then I subtracted f(x) from my original y points to get the auto-correlation.

Then i realized, this is the same method for finding residuals...
I'm very confused with this whole idea of auto-correlation... is it the same as residuals?

Thank you, I appreciate your help in advance

 

[voko]

I do not think you were supposed to do a quadratic fit. Go for the linear one.

You have not done any auto-correlation yet. You need to find the residual after the linear least squares fit, and then do auto-correlation on that.