from Michael Wathen: >To do true Fourier Analysis for this problem you would have to >solve a Three dimensional wave equation (find the equation that >will predict the amplitude for each partial frequency). ....Since it is a three dimensional >problem we would need to know that >shape in two independent planes (shape of the string moving in up >and down, the shape of the string moving sideways). As you can >imagine that is nearly impossible to do. You also need the >velocity of string in each direction. So Fourier Analysis will not >work here and thus we can not predict from this method the spectrum >of a given note (relative strength of partial frequencies). Bob says: Yeah, I probably used the wrong term. An interesting point is still raised here. A "scientific explanation" of any phenomenon can be in an infinite amount of detail, but often some of the finer detail is ignored in order to make a point more clear. For example: I imagine that, as you say, it would be difficult to measure a string's exact shape at the moment of release, but it is possible with optical equipment to measure the string's velocity and direction (in any plane) as the wave passes a single point during the first complete cycle of the fundamental, and therefore to deduce the shape of the "traveling wave." While a string vibrating in free air does so in horizontal and vertical modes (and everything in between), I think an argument could be make for the usefulness of the fact that the bridge/soundboard assembly is certainly more compliant in the vertical mode, and the compression/rarefaction of the air waves can also be thought of in two rather than three dimensions. I think examination of the vertical component is useful enough for our purposes. From what you say, I don't think we disagree about this. >Mr. Davis wrote: >Yes [well, except for the ones which are multiples of the inverse of the >strike point fraction -- i.e., if the string is struck at 1/7 of its length, >the 7th, 14th, etc. partials will be missing]. >My Reply-------------- >Why would this be true? Do you have any idea as to what its physical >explanation would be? "Missing"is probably too strong a term which would be reserved for a naive case -- "considerably attenuated" might be more like it in the real world. As to why partials having nodes at the strike point are suppressed, I'd like to defer to someone else who might explain this better than I. Bob Davis, RPT
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