The h Bar

Basically all books do. Many publishers print books in e.g. India meant for the local market, but obviously they have a market back in the States as they are cheaper.

0celo7

I'm looking at a book for $150 that is $80 on Amazon

why even bother

alarge

10:08 PM

Some are first editions etc. that have value for collectors. Or when it comes to science books, they might have recently been out of print.

Why not bother to try sell the book? I'd sell any of my books for that markup and buy a new one myself if I found someone willing to pay.

Stan Shunpike

@JohnRennie Could you elaborate a bit more on this eigenfunction stuff? I was a little bit confused where that came into play.

0celo7

@alarge well of course I'd be willing to sell at a markup, but who would buy

alarge

@0celo7 I don't know or care as long as they do.

Stan Shunpike

@JohnRennie for example, I thought we only called a function an eigenfunction when there exist an operator such that $Af = \lambda f$. Where do operators come into play with a musical string? I thought those were only relevant for quantum mechanics.

0celo7

abebooks.com/servlet/…

$50 more than on Amazon

not a first ed

alarge

10:11 PM

Sold by Book Depository which is a company Amazon owns.

0celo7

@alarge wait so you've actually had success selling books at these ridiculous markups?

@alarge huh

alarge

@0celo7 No. Never tried. But in general people do buy say computer equipment at markups because they don't know better.

0celo7

@FenderLesPaul right up your alley physics.stackexchange.com/questions/202332/…

alarge

@0celo7 So Amazon owns Abebooks which is a marketplace for (used) books. The sellers are mainly companies or bookstores. Book Depository is one of the largest online bookstores I think, or at least was before Amazon bought it 5-10 years ago or so.

0celo7

Amazon = evil?

the subsidiary sells at a markup

alarge

10:16 PM

@0celo7 It's cheaper sometimes, and they have always shipped for free to anywhere in the world, which is why about 10 years ago I was using the Book Depository a lot.

Nowadays I usually just check Abebooks and Amazon.

0celo7

@alarge Do you have Amazon Prime?

alarge

I did for several years. Not right now, though.

David Z

@StanShunpike not sure what you were talking about with John, but the ideas of eigenfunctions and so on do show up in some classical mechanics problems. Waves in general can often be described as eigenfunctions of some operator or another.

0celo7

I get it through my dad

alarge

I still had to pay postage when buying from US Amazon as my local one didn't have one book I wanted.

Stan Shunpike

10:20 PM

@DavidZ I was talking about harmonics with musical strings.

I am just trying to understand what harmonics are and which equations are pertinent to musical situations.

And I havent seen operators mentioned in any music theory texts that I have read, although I have not ready very many. Probably 50-70. But there are loads of different ones

David Z

Oh, no, you'll never see operators discussed in a music theory text. They don't get very far into the underlying physics.

with maybe a couple of really exotic exceptions

The physics of a vibrating string all comes from the 1D wave equation $y''(x,t) = \frac{1}{v^2}\ddot{y}(x,t)$

Vibrating string

A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note. Vibrating strings are the basis of any string instrument like guitar, cello, or piano. == Wave == The speed of propagation of a wave in a string () is proportional to the square root of the tension of the string () (discovered by Vincenzo Galilei in the late 1500s) and inversely proportional to the square root of the linear density () of the string: === Derivation === Let be the length...

Stan Shunpike

Yeah so why was @JohnRennie mentioning eigenfunctions? Thats why I was confused. Also dmckee mentioned specifying the boundary conditions is important. What does that mean for music? Is that just where the string is tied down?

David Z

Yeah, boundary conditions are the points at which the string is fixed.

You can consider the wave equation to be the operator $\partial_x^2 - \frac{1}{v^2}\partial_t^2$ acting on the function $y(x,t)$. That operator is the 1+1D equivalent of the D'Alembert operator, and its eigenfunctions correspond to allowable waves of the string.

(if I'm not too confused. I might be.)

The boundary conditions affect the allowed eigenfunctions, and in the case of a string, they determine the set of vibrational frequencies - more or less, the possible notes you can make on the string.

Or another way to look at it, the boundary conditions restrict which vibrational modes (i.e. eigenfunctions, more or less) can actually be excited.

alarge

@DavidZ Well, they more like dictate the color of the sound, I think. The pitch comes from making the string shorter by pushing it against the fret board.

David Z

They do that too, but I was thinking more in terms of different notes - you can excite primarily the fundamental mode, or primarily the second harmonic, or so on, and those all correspond to different notes

although I guess it doesn't really work so well on a string. Easier on brass instruments.

Stan Shunpike

10:34 PM

So eigenfunctions corresponds to higher harmonics?

alarge

You can excite them on a string as well by lightly pressing the string at the point of the node.

David Z

@alarge ah okay, good to know. I'm not really a string player.

@StanShunpike Each eigenfunction of the operator which isn't ruled out by a boundary condition corresponds to a harmonic.

Stan Shunpike

Ohhhhhh

Duh

FenderLesPaul

11:01 PM

@0celo7 no, I haven't read any stringy stuff

unfortunately I don't have the interest to do so

I'm more interested in AdS/CFT in the large central charge limit where you basically just need GR in the bulk

0celo7

11:14 PM

@FenderLesPaul do you need string theory to derive that result

FenderLesPaul

not exactly; you do need the concept of a string scale but beyond that it's just the argument that diffeomorphism invariant higher curvature corrections to gravity are suppressed in a saddle point approximation of the partition function and you just get Einstein gravity

the suppressions are in terms of Newton's constant and the string scale