1) That's one possibility. Plans for making a DIY sonometer are
readily available on the web.
One slight problem: The typical HS does not have that kind of shop.
2) For $400 I'd buy an off-the-shelf electric bass guitar and have
a *lot* of money left over.
a) The guitar comes with pickup coils (which are not included in
the PASCO item).
b) The electronic version means students can use headphones so
they don't disturb the rest of the class quite so much.
It also means they can hook the thing up to a PC acting as
an oscilloscope + data logger + Fourier wave analyzer, etc.
c) Use a capo for changing the length.
d) Measure the tension using weights with hooks pulling perpendicular
to the middle of the string. This requires some nontrivial physics
to establish the connection between perpendicular force and
longitudinal tension as a function of displacement. It's nonlinear.
OTOH for HS students you can just give them the formula. They can
verify it easily enough.
More specifically, to achieve a given tension, /choose/ a weight and
then /adjust/ the tuning key to achieve a predetermined /standard/
deflection. This is an example of a feedback loop. It takes the
aforementioned nonlinearity out of the critical path.
To facilitate this measurement, clamp the instrument to the table
using standard chem-lab clamp technology.
e) Strings stretch. If you just measure the unstretched string, you'll
be off as to the mass per unit length. OTOH it is not hard to measure
the stretch and account for it. Hint: put marks on the strings.
f) This saves so much money that you can buy two of everything. This
increases the range of things you can do. Note that you can make
extremely accurate /comparisons/ between frequency A and frequency
B, and/or multiples thereof, even if you don't have exact traceable-
to-NBS values for A or B separately.
You might think that nowadays guitars would have a separate pickup
for each string, but they don't, not in this price range anyway.
I spent many many hours in HS fooling around with various ways of
making Lissajous patterns. I can't pretend I knew what I was doing,
but later I discovered that Lissajous patterns are a well-known and
powerful comparison technique. I read about this in a book called
_Theory of Sound_ by some guy named Rayleigh.
Also I remember once I walked into the lab and a bunch of grad
students were tearing their hair out, trying to figure out how
to find a resonance. I pushed one button on the scope, putting
it into XY mode, current versus voltage. A Lissajous pattern
appeared, and all was revealed. The students gasped appropriately.
So, not all of that high-school fooling-around time went to waste.
g) If you look at all closely, you will notice that the frequency of
the 2nd harmonic is not 2x the fundamental. I know Feynman says
that it is, and indeed that it "must" be, but it's just not.
This is just one of the many things you can do by comparing one
string with another, as discussed in the previous item.
h) IMHO it is better, as a general rule, for students to learn about
real-world stuff, other things being equal. And often things are
unequal, in a good direction. The industry has optimized the cost
and performance to a fare-thee-well, and the development cost was
amortized before you showed up.
I'm not saying that the PASCO price is a rip-off; I'm just saying
that they have huge development costs -- not to mention the huge
cost of sending a rep around to give you a demo -- and they are
providing a service I don't need. YMMV.
Not to mention the coolness factor. A guitar is waaay cooler than