Anders Askenfelt On Pianos

[Richard Brekne]

List, given the doubt surrounding the nature of flexural waves / bending
waves and whether or not they are transverse in nature or not, I asked
Anders for a clarification which he was kind enough to provide me with.
I shall not trouble him again as I think we have enough now to draw a
pretty reasonable good conclusion to the present debate. I also asked
him to put to rest the question of how sound radiates, and he included
the correct definition (of the three alternatives I provided him with)
along with his comments on that.


Anders Aksenfelt writes :

The bending waves I was talking about are identical to flexural waves.
They 
are transversal waves, but that the propagation velocity is frequency 
dependent. This makes them a little more complex than transversal waves
on 
an ideal string, which has a constant propagation velocity. Piano
strings, 
on the other hand, which do have stiffness, have a frequency dependent 
propagation velocity, just like plates. The dispersion phenomenon in a
bar 
described by Dr Russell is easily observed on piano strings.

About radiation: The citation you gave below is correct. Sound is
radiated 
when an object like a loudspeaker membrane, a violin top plate, or a
piano 
sound board is pumping air back and forth.  The appropriate unit for the 
strength of a sound source is [m^3/s], cubic meter per second, in
SI-units.


>Others understand the word radiation as a process of putting air in motion as
>is in line with  transverse movement from the panel.

                                                 Sincerely,

                                                 Anders Askenfelt



The Loudspeaker analogy holds true, and interesting enough he
equivocates this to the violin top plate as well. I found it interesting
that longitudinal waves were given to be the cause of the back and forth
"rocking" of the bridge there has been so much discussion about, instead
of the strings transverse waves. And I find it intriguing to know that
the transverse movement of the panel is such that the propagation
velocity is frequency dependent. I didn't know that, though perhaps that
piece of information has zipped past me once or twice before. 

Any ways gang, though this discussion has taxed the patience of more
then a few, I am personally glad we stuck it out.