Sound waves(a neat experiment)

[John Delacour]

At 9:31 PM +0100 1/17/02, Richard Brekne wrote:

>Why do I insist on the wave front being the direct source of 
>vibration in the panel. Well, for a couple reasons. The speed of 
>transverse bending waves is dispersive.... that is to say that the 
>wave velocity is frequency dependent.

Richard, I've not heard the epithet "transverse" used to describe 
bending waves (flexural waves).  Is that something you have added to 
what you've read?  It seems that these 'bending waves' are indeed 
very significant, but let's get a clear picture of how they behave 
and not adorn them with properties they don't have.

>  Yet we operate with a constant when we use the formula for the 
>speed of sound through wood.

Far from it!  Any wood, but especially fir or spruce, is anisotropic 
and will behave differently in different planes.  If sound waves will 
pass through spruce at nearly 5500 metres per second along the deal, 
its speed across the grain of a quartered deal might be only 1500 
metres per second and if it's not cut on the quarter, then there will 
be other complications.  You were extremely vague yesterday when I 
asked the question about Sitka spruce, and now you are talking about 
formulas and constants.  Ron Overs answered the question briefly but 
did not extend his answer to say that for the good reasons he gave, 
sound propagates faster along the grain in soundboard wood than in 
any other wood.  In Douglas Fir it might travel at only 4900 metres 
per second.

>  That says to me that that formula is referring to a compression 
>wave or perhaps some form of quasi longitudinal wave, as in Rayleigh 
>surface waves for example.

Are you saying that Rayleigh waves are at play here?  Please explain. 
What about brain waves ??

>Also I cant escape the fact that the panel has three dimensions, and 
>any force acting upon that simply has to propagate though all three. 
>I don't see this is in conflict with the 2 dimensionalilty of the 
>panel as a vibrating plate.

That's all very confused.  It's no good just blurting out all these 
great new things; you need to get some sort of understanding of them 
first.  Panels and plates are not two-dimensional.

The reason I was so loth to talk of the vibrations of the soundboard 
from the outset of these discussions, and still am, is that I do not 
have a clear picture of its very complicated behaviour.  Very slowly 
I am getting a better grasp of the elements involved and the picture 
is becoming extremely rich if nothing else.  The more I discover, the 
more interesting and significant it all becomes and I have no doubt 
that for me at least it will have most important design implications, 
contrary to your doubts on the matter.

There are certainly different types of vibration at issue, and owing 
to the non-rigid nature of the system, there is certainly 'movement' 
involved at least as regards the natural frequencies of the board.  I 
don't think any piano man on this list is anywhere near capable of 
the mathematics required to describe accurately all the phenomena of 
the string and the soundboard -- some of the texts I have read are 
quite frightening, involving huge equations including imaginary 
numbers and lots of calculus -- but out of it all it is still 
possible to gain a proper picture in the end and everyone interested 
in this topic will be wiser as a result and, I believe, in a better 
position to make informed design decisions.

Here is an interesting exchange between me and a very well-informed 
acoustician who expresses himself clearly and simply and from whom I 
hope to get more:

>  > c) Given that the system will manifest flexural vibrations at its natural
>>  frequencies (many questions here alone) can it be said also to have flexural
>>  vibrations at the manifold frequencies fed to it from the strings?
>
>You don't have to vibrate a structure at exactly its natural frequency
>for it to resonate. If you are slightly to one side of the natural
>frequency then resonance can still take place. The further you move away
>from the natural frequency, the less resonance you will get. If the
>structure is highly damped then you do not have to be so close to the
>true natural frequency to get resonance. If the soundboard is big enough
>and flexible enough and the damping is sufficient then the modes
>(resonances) overlap and almost any frequency will resonate.

By a strange coincidence I had already demonstrated this the day 
before in the following way:

I struck the soundboard of a strung piano and noted the frequency of 
the fundamental mode very roughly.  I then played the note 
staccastissimo on the piano that corresponded to this frequency and 
heard a sort of distant resonance which I would previously have 
ignored.  Playing notes a semitone or a tone each side of this, I 
noticed I got a similar resonance and was prepared for disappointment 
until I then played notes four or five tones distant from the 
resonant note and discovered that the resonance was practically 
absent.  It is interesting that while this resonance is quite clearly 
perceptible when you are listening for it, it does not give undue 
loudness to the notes affected, though I presume that it might in a 
less well designed piano.  Very interesting.

JD