Topic: Post about phase of lateral and transversal vibrations in guitars
Alan Carruth is a classical guitar luthier who is apparently known for his detailed examination of the physics of the guitar sound board. Interesting series of posts in a discussion of controlling the two two frequency modes on a classical guitar. Note that he is writing about the transmission of vibrations through and across the wood (with the grain and against it) not the vibrations of the strings.
http://www.classicalguitardelcamp.com/v...p?t=101819
I believe he has written more about guitar soundboards, but I have not been able to find his work quickly. Of course, he is talking about guitars, which have a different bracing pattern, so I do not know how much of this applies to a piano sound board, which may also be so thick that cross-vibrations are limited.