bill at h...
Thu Jan 15 22:09:02 GMT 2004
> It is probably a bit of a sauce to ask but
> what experimentation was carried out on the
> Leigh and Perrins bell?
For a summary of Perrin, Charnley and DePont's work see
http://www.hibberts.co.uk/pandc.htm and associated pages. The actual
paper runs to 21 pages (it's not on my website). The research
comprised an absolutely exhaustive analysis of the vibrational modes
of this particular bell, by stimulating it with a signal generator
and probing all over the bell to identify nodes and antinodes. They
identified 134 different modes of vibration, many of them split as
doublets. They then built a computer model of the bell using finite
element analysis, and adjusted the model until it produced the same
modes of vibration, to confirm their understanding of the nature of
each mode. These two pieces of work must both have been enormous
Based on the analysis, they proposed a classification scheme for
vibrational modes of bells which is utterly comprehensive, I don't
believe there is anything more that could be said on the subject!
What they did not consider in their research was the significance in
the heard sound of this multiplicity of modes. For instance, some of
the modes are torsional, i.e. they involve the bell twisting about
its vertical axis, and these modes radiate no sound into the air.
What I did a couple of years ago is compare the P&C results with an
actual recording of the bell and link the P&C classification scheme
to what we hear when a bell rings.
This linking has been enormously useful to me because I now know the
physical origin of each partial detected in a bell's sound. This
provides an understanding of which modes are directly stimulated by
the clapper blow, and which are 'sympathetic' vibrations (such as the
quint) into which energy flows as the bell continues to vibrate. This
was an essential step towards finally understanding the origin of the
strike note. The partials I described as 'strike partials' in my
recent RW article http://www.hibberts.co.uk/rwstrike.htm are those
which Perrin et al identified as 'rim' partials, i.e. with an
antinode at the soundbow, i.e. maximally stimulated by the clapper
The work they did could also in principle be linked to Lehr's work on
tuning - see http://www.hibberts.co.uk/lehr.htm which documents his
experiments on how taking metal off at different points inside the
bell affects the tuning of all the key partials. I am not aware that
anyone has ever attemped this.
Saucy enough for you?
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