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Re: [Phys-l] Curve fitting versus averaging [was question on averaging]



As adv. lab. mgr this is similar to the method "we" introduced to measure "2nd" sound. i.e. plot and fit. No "high powered" faculty member objected to this method.
Perhaps important (I pray not.) Instead of changing the cavity length (very impractical) "we" changed the frequency.

bc i.e. bc agrees w/ the chemist and prays he's not having another Sr. moment.

p.s. Dispersion, if any, was not obvious.

On 2009, Feb 19, , at 06:45, Edmiston, Mike wrote:

At the end of his post on averaging, John Denker said, "Also note that
"averaging" is a lame substitute for curve-fitting." I agree with this
statement. I want to describe what might be a good and interesting
example, but I have been too lazy to think it completely through, and I
might be all wet.

Suppose you want to measure the speed of sound by finding standing waves
in a tube. You have a Plexiglas tube with a speaker and microphone at
one end, and a movable plunger at the other end. You drive the speaker
at fixed frequency and move the plunger in or out and find the locations
where the sound is loudest or weakest. You can do it just by listening,
or you can look at the magnitude of the microphone signal, or better yet
you can hook the oscillator and the microphone to an oscilloscope in XY
mode and look at the phase relationship.

Anyway, suppose you can find "n" plunger positions that give resonance.

The typical student just wants to find the differences between these
positions and average the differences to find the average
half-wavelength. However, doing this actually only utilizes the first
and last position because all the intermediate positions drop out during
the averaging process. This means you are wasting your time to find all
those intermediate resonance points.

This strikes the students as odd. Surely having all that extra data is
good for something. Actually all that data is indeed worthless if you
simply take differences and average the differences. But it seems
curve-fitting might be a way to utilize all the information. Plot the
resonance positions against "n" or an integer index number, and fit a
linear regression line to the positions, and use the slope as the length
of one-half-wavelength. It seems this would be using all the points and
would give a better estimate of the half-wavelength than just taking the
difference between the first and last positions and divding by the
number of half-waves between those two positions.

Am I looking at this correctly?


Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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