Waves

[John Delacour]

At 8:37 PM -0500 13/2/02, Greg Newell wrote:
>I tried to resist but I think I'll have to jump into the fray for a
>quick question / observation. If in a solid wood panel soundboard the
>waves go with the grain at least better than they do against, which
>direction to they go in a laminated board? Really not trying to be cute
>(trust me that's not possible) I really want to know.

It's not a question of which direction they go but how fast they go 
in the various planes.  The stresses set up by the undulations of a 
laminated spruce or fir board will be different and the coupling of 
longitudinal waves and flexural waves will be different.  To find out 
just how different would require some very clever measurements and a 
lot of well-conceived experiments.

Don't take these figures as gospel, but they give some idea of the 
relations between the quantities at issue...

Longitudinal waves _at_any_frequency_ will travel along the grain of 
Sitka spruce at say 6000 Metres/sec and across the grain at only 1500 
M/s.  The speed of the flexural waves is related to these speeds but 
is much slower and frequency dependent.  My calculations may be way 
out, but for the eight A's of the piano the speed of the bending wave 
carrying the fundamental might be a parabola giving

52 77 104 147 208 309 415 587 Metres/second

The less the stiffness, the lower the speed of A1 27.50 c/s and the 
shallower the parabola.

Sound waves in air (longtudinal waves) travel at about 345 M/s and 
acoustic radiation from flexural waves is efficient at speeds above 
this.

The modal undulations and contorsions, which can be regarded as 
standing waves, it seems to me, rather as a cat on a hot tin roof can 
be regarded as standing, are also dependent on these speeds.

How these different wave forms interact or couple with each other is 
beyond me to describe at the moment, though I have a far better 
picture of things than I had a few months ago.

JD