Thank you very much Mark for this level-headed,
dispassionate discourse. This is how I have always
undersood things to be.
Thump
--- Mark Kinsler <kinsler33@hotmail.com> wrote:
> I don't know if postings from a non- (or not-yet)
> technician are permitted
> here, but I believe I can contribute a bit of
> engineering insight here that
> could clear things up.
>
> Mechanical impedance is the result of the
> springiness and inertia of a
> mechanical part. Your sounding board has some
> inertia due to its mass. It
> also has some springiness. Wood (and most other
> materials in a piano) will
> push back in direct proportion to the amount of
> deflection applied to them.
> (Exceptions: felt and buckskin, by design.)
>
> The sounding board's springiness derives from the
> behavior of wood in
> compression and bending. From an engineering
> standpoint, a crowned sounding
> board that's glued at its rim to a rigid piano frame
> is an arch. When you
> push down on the crown of an arch, the ends of the
> arch try to spread.
> (This force is due to the downbearing of the strings
> on the bridge.) Since
> the arch 'ends' (in this case, the glued rim of the
> sounding board) cannot
> move, the material of the arch is compressed. Wood
> in compression behaves
> like a spring.
>
> The situation is really a bit more complex than this
> because of the
> stiffening ribs. These experience bending stress,
> but also behave like a
> spring. It doesn't matter very much from a purely
> physical point of view,
> but since the wood in a crowned sounding board is
> under compression, we get
> a somewhat stronger structure since wood is a bit
> stronger in compression
> than in tension, especially across the grain.
>
> I don't think I've told anyone here anything new
> thus far. But there's a
> bit more.
>
> If the impedance of two coupled mechanical
> parts--say the string and the
> sounding board--are different, any energy applied
> from part #1 will not be
> completely transferred to part #2. What happens to
> the energy that's not
> transferred? It isn't lost: it is _reflected_ back
> into part #1.
>
> In a piano, the impedance of the string is different
> from that of the
> sounding board. Thus part of the energy imparted by
> the hammer to the
> string is reflected back into the string. We want
> this to happen: it's what
> makes the string keep vibrating. If all of the
> energy from the string went
> into the sounding board, we'd hear only a dull thump
> instead of that
> splendid ringing sound.
>
> The piano is a highly efficient system.
> (System=chain of parts.) The energy
> that's reflected back into the spring is not lost,
> but stored in the
> vibrating string. It is transferred to the sounding
> board gradually, on
> each vibration.
>
> Could the sounding board have a negative crown (like
> a dish), and the
> downbearing be "upbearing?" From a physical
> standpoint, yes. There would be
> no difference in the behavior of the system, though
> the bridge would peel
> off the sounding board pretty quickly and the design
> of the bridge pins
> would be interesting.
>
> Or, in another possible configuration, could the
> sounding board have a
> negative crown and the downbearing still exert force
> downward? Again yes.
> (The bridge would have to be rather high.) The
> sounding board's wood would
> be in tension and the rim of the sounding board
> would tend to be pulled away
> from the frame, but again from a purely physical
> standpoint the system would
> work about like a normal piano. Structurally, of
> course, this configuration
> would be a disaster, but the sounding board and
> strings would behave pretty
> much normally if the whole works didn't peel apart.
>
> The relationship of the sounding board to the
> outside air is a bit more
> complex than the relationship of string to sounding
> board. Ideally, we want
> the impedance of the sounding board to match that of
> the outside air. This
> makes the piano loud enough to hear. And the
> sounding board does just that:
> it's an 'impedance matching' device that tries to
> match the impedance of the
> strings to that of the air. (Side note: the bell of
> a brass instrument is
> also an impedance matching device.)
>
> >From an efficiency standpoint, we do not want
> energy from the air to be
> reflected back into the sounding board. From an
> artist/craftsman
> standpoint, we _do_ want this to happen, because
> that's part of what gives
> the piano its tone.
>
> It's also worth examining the resonant frequency of
> the strings vs. that of
> the sounding board. The resonant frequency of each
> string is obvious to
> anyone. The resonant frequency of the mounted
> sounding board is known to
> the technician, who can determine it when the piano
> is unstrung: only one
> note sung into the unstrung piano will resonate
> loudly, and that's the
> resonant frequency of the sounding board. (This is
> the simplest case: a
> real sounding board will resonate at several
> different frequencies. The
> resonant frequency of the sounding board will also
> change somewhat under the
> force and mass of the strings.)
>
> We really don't want the resonant frequency of the
> sounding board to be a
> large factor in the behavior of a piano. Ideally,
> the sounding board should
> be forced to vibrate at the frequency of the struck
> strings. In practice,
> however, this is not the case. I don't know if the
> terms are equivalent
> from one sort of instrument to another, but in the
> bowed string instruments,
> we get what's called a 'wolf' tone when the string's
> resonant frequency
> approaches that of the sounding board. On the
> 'cello, this occurs at the F
> played on the C string. I have read about 'wolf'
> scales on the piano, and
> perhaps this is the same phenomenon.
>
> So as it happens, the resonant frequency of the
> piano sounding board is a
> factor in its behavior, but it's not necessarily a
> bad thing: it contributes
> to the overall tone of the instrument, as do all the
> other 'imperfections.'
>
> I have read the other posts in this thread, and it's
> clear that everyone has
> a good understanding of these concepts. However,
> descriptions, terms, and
> experiences vary, thus making the various
> contributions appear inconsistent.
> What I've given here are the terms used in
> engineering and physics. I
> gladly defer to the experience of the craftsmen who
> read this list. A far
> better treatment of the matter is given in an old
> Scientific American
> article called 'The Physics of the Piano.' I
> believe that the complete
> reference is given in Art Reblitz' textbook.
>
> Mark Kinsler
> 512 E Mulberry St. Lancaster, Ohio USA 43130
> 740-687-6368
> http://home.earthlink.net/~mkinsler1
>
>
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