From: Kevin Austin (kevin.austin@videotron.ca)
Date: Sat Jan 22 2011 - 13:21:17 EST
I think that what you describe is only part of the question.
The 'ideal' non-physical string, touched at an infinitesimally small point at exactly the mid-point of a string [given other limitations], should behave as you describe. But the physical world is not virtual, and there are other features.
Among the first would be the manner of excitation of the string. If it is done with a bow [a dry friction stick / slip method ...]
and the bow has to be 'somewhere' on the string, forcing this place to vary between being a node and an antinode. Effectively, the bow is a lowpass filter, and (more or less) forces the violin string into a trangle wave-like vibrational mode. [There are images of this on YouTube.] Note that a triangle wave contains odd harmonic partials that fall off at the rate of 12dB/oct.
The strong is also not a 'perfect' medium, as in the bowing, it gets pulled (lengthened), and released (shortened), and the tension it is under varies accordingly. I read that these two opposing forces more or less cancel each other out in perfectly formed strings.
Also, the ends of the strings act more like cantilevered hinges that 'fixed point' hinges, and that the string near at the ends adds non-linear straightening forces (rigidity).
This to say that the 'ideal' string doesn't exist, and there are many reasons why upper partials are generated more weakly.
etc
Kevin
On 2011, Jan 22, at 7:05 AM, peiman khosravi wrote:
> On that note I have another question. My acoustic books say that by lightly touching a node on a vibrating string we stop all the modes of vibrations that do not have a node at that point. As a violinist this has been intuitive to me in the past but recently I got thinking:
>
> Touching the string halfway through you should be getting not only the second mode of vibration (second harmonic) but also the 4th, 6th, 8th and all the other odd harmonics. But my ears and intuition have always told me that we do only get the second mode of vibration in the above case. What is the explanation? The 4th mode of vibration also has a node halfway through the string so why is it stopped? Is it the case that in fact the touched node must be the first node (of a given mode) measured from the fastened end of the string?
>
> Thanks
>
> Peiman
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