compression waves

[John Delacour]

At 1:07 AM -0500 11/21/01, Stephen Birkett wrote:

>What i did say is that I believe  [!!] bridges are transparent to longitudinal
>modes.........highly unlikely that any external clamping mechanism 
>will be able to prevent the internal wave transmission past it, as 
>long as the molecular structure is continuous. Transmission waves 
>simply pass right past these clamped bits. They will eventually be 
>reflected when they reach the geometric and physical _end_ of the 
>bar, or localized discontinuities.

This contradicts Conklin's finding (which I have verified) that the 
frequency of the wave is a function of the speaking length.  As I 
mentioned yesterday, the propping up of the speaking length with a 
_simple_ bridge, by which I mean the equivalent of a low violin 
bridge, is of course adequate to change the base frequency of the 
transverse waves but will not affect that of the compression wave. 
By contrast, anything in the nature of a firm clamp, which includes 
the clamping effect of a piano bridge, does serve as a termination 
(broadly speaking) of the wire with respect also to the main 
compression wave.  I say nothing of its harmonics, since I haven't 
tested these.

A wire of about a metre is stretched between chuck and hook on a 
string-making machine at a tension ca. 80 lbf.   Points are marked on 
the wire to indicate the position of a simple bridge, or 'nut', for 
pitches of semitones C through G.  A 'clamp' consisting of two 50 mm 
flattening dies in a 'bottle' moved to these positions will, of 
course, have the same effect on the pitch of the note as the simple 
bridge.  I now move this bottle to a position such that I obtain _a_ 
C from the compression wave and file the wire.  I move the bottle 
along to get C# and so on up to G, marking with the file as I go.  I 
now have two sets of marks representing the scale for the two 
'modes'.  The two sets occupy different extents of the wire but are 
similar in their progressions.  I don't need to give numbers for it 
to be clear that for any given tension of the wire it would be 
possible to choose a speaking length that would produce a harmonious 
relationship between the base frequency of the two waves.  This is, 
broadly speaking, what I take to be the principle of Conklin's method.

I have to go out now and haven't time to respond to the rest of your 
very interesting post, but will do so later.

JD