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Thus far, I have had two seperate dreams involving pipe organs. While I
was learning about organ terminology, I had a dream about playing a pipe
organ. When I started learning about the stop names, I had a second
dream in which I accidentally killed 3 people by choosing a powerful stop.
I just read that the speed of sound in air is around 340 m/s, and that
an open pipe contains 1/2 of a wave while a stopped pipe contains 1/4 of
a wave. (Not forgetting the end corrections due to the stationary air
outside the pipe.) And also that long thin pipes have more harmonics
than short wide pipes.
All of this has pretty much inevitably ended with... the wave equation.
Yah.
So apparently the wave equation tells us that the 2nd derivative of some
physical quanitity "u" with respect to time is equal to the square of
the wave propogation constant multiplied by the Laplacian of "u".
...which would probably mean something if I could figure out what a
Laplacian is! :-S
According to Wikipedia, the Laplacian of u is the sum of all partial 2nd
derivatives of u with respect to every coordinate axis.
...so...the total curvature then? ._.
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> All of this has pretty much inevitably ended with... the wave equation.
Hehe, I so knew that was coming.
> So apparently the wave equation tells us that the 2nd derivative of some
> physical quanitity "u" with respect to time is equal to the square of the
> wave propogation constant multiplied by the Laplacian of "u".
>
> ...which would probably mean something if I could figure out what a
> Laplacian is! :-S
>
> According to Wikipedia, the Laplacian of u is the sum of all partial 2nd
> derivatives of u with respect to every coordinate axis.
>
> ...so...the total curvature then? ._.
Pretty much yeh - the wave equation basically says that the 2nd differential
in time is proportional to the 2nd differential in space. Obviously the 2nd
differential in "space" depends on how many dimensions you are working in,
but you more or less just sum up the 2nd differential in each dimension.
Thinking of writing a simulator? ;-)
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scott wrote:
>> All of this has pretty much inevitably ended with... the wave equation.
>
> Hehe, I so knew that was coming.
Yeah, pretty much.
>> ...so...the total curvature then? ._.
>
> Pretty much yeh - the wave equation basically says that the 2nd
> differential in time is proportional to the 2nd differential in space.
> Obviously the 2nd differential in "space" depends on how many dimensions
> you are working in, but you more or less just sum up the 2nd
> differential in each dimension.
Hmm. Seems simple enough...
> Thinking of writing a simulator? ;-)
Well let's put it this way: What do you think my chances of building a
working set of organ pipes are? :-P Last time I tried to cut wood, I
couldn't even cut it straight! :-/ I figure I have far more chance of
building an organ simulator...
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Some dream, huh? Only a math/musician to dream of organs and equations... :P
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nemesis wrote:
> Some dream, huh? Only a math/musician to dream of organs and equations... :P
For the record: I have never had dreams about equations.
Dreaming about people being killed is unfortunately very typical for me
though. :-S
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Invisible wrote:
> Hmm. Seems simple enough...
Well, I just implemented it, tried it, and... it doesn't work at all. :-.
Oh, wait... *second* derivative! >_< Damnit...
Oh look, and I've also implemented u = c d2u/dx2 rather than d2u/dt2 = c
d2u/dx2. I'm doing well here. :-/
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> Hmm. Seems simple enough...
>
>> Thinking of writing a simulator? ;-)
>
> Well let's put it this way: What do you think my chances of building a
> working set of organ pipes are? :-P Last time I tried to cut wood, I
> couldn't even cut it straight! :-/
Just practise, and you can buy (or make) some jigs that constrain the saw to
move exactly straight. THat way you will get perfect cuts every time.
> I figure I have far more chance of building an organ simulator...
You reckon? Thinking about it, I think you will need to use the
Navier-Stokes equations, because you need to simulate the velocity of the
fluid too, not just the pressure. (the velocity of the air stream is what
causes the pressure differences which in turn cause the flow to oscillate
between going out of the mouth and staying within the pipe).
Good luck :-)
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48fdd79e@news.povray.org...
> Just practise, and you can buy (or make) some jigs that constrain the saw
> to move exactly straight. That way you will get perfect cuts every time.
Let's add that a plane is always meant to be checkered :-)
Marc
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48fdd966@news.povray.org...
>
> 48fdd79e@news.povray.org...
>> Just practise, and you can buy (or make) some jigs that constrain the saw
>> to move exactly straight. That way you will get perfect cuts every time.
>
> Let's add that a plane is always meant to be checkered :-)
> Marc
is NOT always :-s
Marc
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>> Well let's put it this way: What do you think my chances of building a
>> working set of organ pipes are? :-P Last time I tried to cut wood, I
>> couldn't even cut it straight! :-/
>
> Just practise, and you can buy (or make) some jigs that constrain the
> saw to move exactly straight. THat way you will get perfect cuts every
> time.
Frankly, first I need to find a saw that isn't blunt.
(Actually, finding any kind of tool isn't easy. My mum *has* millions of
tools - every time she goes to start another job, she can never find the
tool she wants, so she buys a new one. It gets used once, and is never
found again.)
>> I figure I have far more chance of building an organ simulator...
>
> You reckon?
I said "chance". :-P
> Thinking about it, I think you will need to use the
> Navier-Stokes equations.
>
> Good luck :-)
Actually... it's possibly not directly related, but Wolfram showed a
trivially simple cellular automaton which has no sophisticated
properties encoded into it, and isn't even an accurate simulation of any
physical system, and yet exhibits the same characteristics as a flowing
liquid. (Most particularly, it has both laminar and turbulent flow.)
This is much simpler to model then exotic differential equations. OTOH,
it's a few orders of magnitude less efficient too... ;-)
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