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Eigenfrequencies... Huh?


Daklu

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Posted

So I finally got a day off yesterday and for some odd reason started skimming through my copy of Standard Mathematical Tables and Formulae [Zwillinger]. I'll be the first to admit that I'm no mathematician. I usually don't have the patience (or interest) to sort through all the formalized symbolism so there is a lot of stuff in there I don't understand. But when I ran across this bit of explanation about eigenfrequencies the only thought I could muster was, "uh.... what?"

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Posted

Not sure I'll be able to make that clear, but when you hit a drum, a bell (or any object actually), it emits a sound composed of a series of frequencies which are the eigenfrequencies. Those frequencies depends on many things like the material the object is made of or its shape. (That's why a small bell sounds differently than a large one). Now, there is no unique dependence between shape and frequency: 2 different shapes can produce the same sounds. And I guess that's waht your book tried to say by "you cannot hear the shape of a drum". (although you could hear if it is broken or not by looking at harmonics, but I won't go there).

hope that's help...

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Posted

That sounds reasonable. It seems odd the book just made the statement without any explanation, unless that methphor is commonly used when teaching eigenfrequencies?

Posted

I am working in the field of acoustics/ultrasonics so it is the way I use eigenfrequencies the most, but I am not sure it is obvious for anyone alse

Posted

Having read your post before pylb gave an explanation, the concept made sense but I doubt could have explained it as well as he did. That, and I assumed what I was thinking was too simple ;)

Posted
This begs the question, can I smell the color of a fruit?

Only as well as you can taste it :D

Extended into the physical/philosophical world, the idea is the same: armed with the knowledge of only the destination, one cannot know the path of the journey. Therefore, the ends may, or may not, justify the means.

Posted

One of the things clear to me (and my german/dutch neighboors) is the meaning of Eigen. It means 'Own' in dutch, however I remember that eigenvalues was named by a German physicist. (wikipedia says: David Hilbert)

Ton

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