Does a piano soundboard have less impedance near the center?

This is one for Mr. Modartt Jake.

My take is that the soundboard is like a big wooden drum head.  Like any thin membrane that is fixed at the edges, the centre is the most compliant, and the very edges not compliant at all.  This much I know from being a structural engineer (sometimes I have to analyze the stiffness and strength of a thin flat floor slab which is essentially the same problem).

As for the cross-ribs, I think they are required because in the cross grain direction, wood doesn't have enough stiffness to transmit vibrations efficiently.  Again the parallel is a wood joist floor - we put cross-bracing from joist to joist to transmit vertical (shear) forces.

I would think that the ideal soundboard would have identical properties in both directions (like plywood).  Which has been tried with somewhat disastrous results.  The cross plies deaden the transmission of vibrations.

I suspect that researchers are still looking for a material that is stiff enough, resilient enough, yet doesn't absorb too much energy, and responds to all frequencies.

So far Sitka Spruce has been the best (with ribs).

Glenn

Just occurred to me: The tapering of the soundboard towards the edges is actually a thickening towards the center, increasing its impedance to more closely match that of its edges?