an analysis of downbearing, etc.

[Richard Brekne]

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Hi Mark. Nice contribution :)

a few comments in blue below

Mark Kinsler 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.
>
Interesting that you bring up the arch thing in this context. It seems 
to be the prevailing train of thought amoung many here that the 
soundboard is not an arch,... ie from another poster..

    "I sort of remember this, but not the details. I'll try to find it.
    Incidentally, the edges won't move out - they'll move in as the
    board is depressed. It's not an arch, it's a cable suspension.
    Remember?"

I dont remember all of the agumentation for this... much of it was very 
convincing... but I dont think it took into consideration that the panel 
will compress uniformly, as a whole in response to downward pressure... 
rather I think, tho somebody may surely correct me here, it was assumed 
all the brunt of any outward movement would be bourne by the edges, 
which would immediatly crush and eliminate any arch like support equally 
immediatly.

> 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.


We dont call them Wolf tones... that refers to a temperament issue. But 
the issue of board reasonant frequencies that closely coincide with 
string frequencies is dealt with fairly well in the 5 lectures on piano 
acoustics... which perhaps may be of interest to you.

http://www.speech.kth.se/music/5_lectures/contents.html

Read the articles by Wogram and Conklin.

>
> 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

Cheers
RicB

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