Eigenfrequencies... Huh?

[Daklu]

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?"

[pylb]

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...

[Daklu]

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

[pylb]

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

[asbo]

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

[Phillip Brooks]

Considering that my math skills are roughly those of a 5th grader, I wanted to know where it came from. This wikipedia entry has the history and some details...

http://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum

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

[crelf]

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

Only as well as you can taste it

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.

[crelf]

So I finally got a day off yesterday and ... started skimming through my copy of Standard Mathematical Tables and Formulae...

Wait, what?!?

[Ton Plomp]

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