Re: [Phys-L] Sonometer, What Do You Think of the PASCO Model?

[John Denker <jsd@av8n.com>]

On 07/29/2014 11:27 AM, Bill Norwood wrote:

> Seems I have heard of a device which will deflect a taut wire between two
> pegs and ...

That definitely exists.
  http://www.parktool.com/product/spoke-tension-meter-tm-1

I don't own one, but every so often I think about getting one.
I can true a wheel by sound and by feel, but the scientist in
me would like to measure something........

Interpreting the tensionometer reading as an actual tension
involves looking stuff on a calibration chart, which is more 
complexity than I would like to see in a high-school sonometer 
experiment.

> But wouldn't it be easier to just take a force probe and pull a string to
> the side by just 1.00 millimeter and then calculate what the tension must
> be?
>
> Thanks for any further elucidation.

Well, that's basically what I was suggesting.  Sorry for the lack
of clarity.

The basic idea is simple.  There are no major difficulties, just 
the opportunity for minor optimizations.

One optimization starts from the observation that you do not need
to add a transverse scale with all possible markings (1.00 mm,
1.01mm, 1.02mm, 1.03mm, et cetera).  Instead, mark just one or
two displacements, and put all the variability into the transverse
/force/ measurement.

To repeat:  You don't need a variable force /and/ a variable 
transverse displacement.  One or the other will do.  I recommend
variable force and standardized displacement.  Assuming metal
strings, you can use an electric touch-detector, and measure 
the force required to cause the string to just barely touch.
This is more sensitive than trying to eyeball the displacement.

As a second optimization, the fixed-displacement trick takes 
the nonlinearity out of the critical path.  We care about the 
longitudinal tension.  That is a spectacularly nonlinear function 
of the transverse displacement (at any given force), but a 
/linear/ function of the transverse force (for any given 
displacement).  This is why I recommend variable force and
fixed displacement, rather than vice versa.

> In my perception it would basically ruin the experiment if one had to hang
> tens of kilograms of weight off the end of the bass guitar.

We agree that would be the wrong way to go.  That's definitely
not what I was suggesting.

Again:  I am suggesting an unmodified guitar, plus slightly
optimized procedures for calibrating the tension.

> Are you saying that one can calibrate via amount of string stretch per
> guitar thumb screw turn, and that one will know forevermore what force is
> being applied to a particular string.?

Also not what I was suggesting.  That never occurred to me.
I don't see how to make it work as an absolute calibration.
On the other hand, something like that might work as a scheme
for /interpolating/ between calibrated points.  Maybe.  It
might be worth looking into, if you have a student who wants
to go nuts with it.  Watch out for lash and hysteresis in 
the tuning key mechanism.

=====================

On 07/29/2014 10:41 AM, I wrote:

> >  You might think that nowadays guitars would have a separate pickup
> >    for each string, but they don't, not in this price range anyway.

That might not be entirely true.  As a proof of concept, you
could buy a piezo electric hexaphonic pickup bridge and stick 
it onto an existing guitar.  For example:
  http://www.bluestarmusic.com/LR-Baggs-T-Bridge-Tune-o-matic-Piezo-Bridge-Pickup-Gold_p_99.html

That's a lower bound on what you can do, and an upper bound on 
the price.  Better solutions probably exist.  I haven't fully
researched the issue.  Somebody should look into it.  Also keep
in mind that it is a moving target, i.e. the answer will change
as a function of time, almost certainly changing in the good
direction.

In any case, just buying two guitars remains a non-ridiculous 
option.  It's guaranteed to suffer less from sympathetic vibrations, 
compared to the single guitar / hexaphonic pickup option.