compression waves

[Ron Nossaman]

I did some investigative thrashing today, and have some observations. Being
electronically challenged, my measuring equipment consisted of a magnetic
pickup from an old electric guitar, and my spectrum analyzer. With piano
type bridge in place on my crude monochord, with a speaking length of
148cm, and a rear duplex of 64cm. I considered only these two lengths in
this experiment. Stroking the speaking length with a rosined leather, I
could produce four different distinct pitches (back muted), depending on
force applied. The only one of these I could detect in the speaking length
with my magnetic pickup was the lowest tone produced with the tightest grip
on the wire, at roughly ten times the transverse. I could pick up the
transverse quite easily even though it wasn't nearly as loud as the
longitudinal. Obviously, the longitudinal wave wasn't moving the string
through the magnetic field like the transverse. Again stroking the speaking
length, I got about the same pitch from the rear duplex. A wave of some
sort does get past the bridge if it is of high enough amplitude in the
speaking length, but I still can't tell if it is passing the bridge, or
shaking the system enough to re initiate a new wave on the back side of the
vibrating bridge, which I still suspect. None of the higher pitches
produced in the speaking length showed up in the duplex unless the
longitudinal speaking length fundamental did. Again, if there wasn't a lot
of violence involved, it didn't pass over.


> As I see it the items on the table are:
>
>1.  Are longitudinal modes in a real piano string determined
>by the speaking length or the total length?

Speaking length, with a touch of weirdness.


>2.  Are the vibrations in the 'duplex' portions of the string
>caused by transverse vibration of the speaking length of the
>string and/or soundboard or by longitudinal vibration of the
>string, which seems to be caused by unknown means?

I still think it's bridge and soundboard movement, unless someone else has
better measuring devices more suited to the job. I seem to have reached my
limit short of doing any good. 


>3.  Are the vibrations excited in the duplex portions
>transverse or longitudinal?

They pretty much have to be transverse. The longitudinal frequencies are
too high and short lived in typical duplex lengths.


>4.  Do the vibrations in the 'duplex' portions of the string,
>caused by whatever means cause the speaking length to vibrate
>in its own fundamental and harmonics or in the fundamental
>and harmonics of the 'duplex'?

To get the duplex to reproduce the fundamental and harmonics of the
speaking length longitudinal, I had to make the speaking length really
screech far beyond what a hammered string could possibly produce.
Transverse in both, by a considerable margin.


>If this summary is correct would someone please explain to me
>how answering any or all of the above questions would
>influence the scale design of a real piano.
>
>Phil

Is that yesterday's, today's, or tomorrow's piano? If we knew what it is
that we have now, it might indicate to us where to go next.

Since definitive proof is apparently beyond my capacity to produce, I'd
just as well throw in another observation that has only been brought up in
passing, that I think is  important. Both the hammering on the end of a
free rod, and rapping a stair rail (or guy wire) have been used as examples
of how to produce longitudinal waves, but they aren't the same. An end blow
to a rod will form a compression wave, but hitting the stair rail, guy
wire, or piano string makes a longitudinally traveling transverse wave -
whatever the technically accurate name for it may be. It's still a
longitudinal wave, but not an internal compression wave, and seems to me to
be far less likely to pass straight through a bridge, and far more likely
to displace the bridge and soundboard vertically than would a compression
wave produced by stroking a string. The other alternative being the
compression wave bulling the bridge fore and aft to re-initiate the
compression wave on the back side. The "traveling transverse" looks like
the best bet to me, and even does the magic conversion from longitudinal to
transverse at the terminations. The pitch being determined by the speaking
length + mystery factor in this case would mean that the mystery factor is
a non rigid termination that lowers the frequency and absorbs the wave
energy quickly. You can gear the wave going back and forth along those
stair rails and guy wires because they're anchored to more high impedance
terminations than a piano bridge and soundboard. 

So there's my contribution. Another wave form to consider. 

Ron N