Immediately after posting the above, I realized that distance could be measured to the film/sensor plane--
which does not move. The focus equation 1/B + 1/D = 1/f becomes 1/(f + delta) + 1/(D - (f + delta)) = 1/f
Unfortunately, this isn't any easier to solve, so far as I can see.
This problem arose in modeling camera focusing movement, such as a control system might do.
It assumes a simple (thin) lens, rays close to the optical axis, and monochromatic light. While most camera lenses are not simple, this is a first approximation.
Camera lenses project an image of a...
Here's a non-math challenge: Build an AI that can beat the new non-Capcha test -- the one that says "Click all the photos containing <X>"
where X is "cars", "street signs", "animals" or some other common noun.
This test is designed to be difficult for machines: it requires both pattern...
Here are the steps to extend the network analog to an ocarina:
Case 2. Piston-drive Helmholtz Resonator (simple conceptual model of fipple)
* Active: piston in base excites oscillation
* One neck
* No flange
* No listening hole
.----.
/ \
------' `...
Here's my understanding of Fletcher and Rossing's analysis of the simple Helmholtz resonator using the network analog. It eventually derives the familiar formula for resonant frequency. This is the *simplest* case!
Network analog:
[Fletcher and Rossing 1998, p. 227]
Thus, instead of Ohm's...
This is going to take a while. *The Physics of Musical Instruments* is a 756 page reference book, but each section depends on earlier sections.. There is no index of symbols, and symbols are introduced (often without a formal defitiion) and then used 30 pages later. So you have to read the...
P.S. For anyone who thinks pitch is frequency, here's a link to a musical pitch that rises endlessly, but never gets any higher (the Shepard tone). Music is all about the ear, brain, and culture.
ttps://www.youtube.com/watch?v=BzNzgsAE4F0
Or maybe..."It's all about that bass-- fundamental...
Got the book. It's *wonderful* -- a treasure trove of acoustics applied to musical instruments: real physics, no "hand waiving". I highly recommend it to anyone interested in the subject of how musical instruments make sound. Darned well worth it. The subject is developed from the basic...
Thanks, Tom. That's an interesting blog. It has empircial data on how temperature and pressure affect pitch, but no formulas. Unfortunately, the author is not a physicist and doesn't try to explain his results: no math, no citations.
He plots pitch against temperature, and finds that the...
OK, let me try it this way: does anybody have an formula for the pitch of an ocarina?
An ocarina is a type of vessel flute that has been independently invented by many different cultures.
Ordinary flutes are air colums (standing wave), but the ocarina works on the principle of a Helmholtz...
Nope. Optical stuff: exposure control, Zone System, shutter calibration, depth of field and opitmal focus, filter calculations, pinhole calculation, large format. Photography, not image post-processing Optics.
In case you're interested:
Photoshop is wonderful--especially for color...
It's an interesting question, but it presupposes:
1) that there is some output from a computer which would mean "I understand what a prime number is.", or even, "I understand what an integer is";
2) that numbers (abstract mathamatical objects, possibly infinite) can be "fed" into a machine...
P.S. The tower acts as a pressure regulator, as well as storing water.. It's a form of standpipe.
There has to be either a tower or pressure tank in the system, because as I said, water is not compressable. Otherwise, the water in your pipes would act like hydraulic fluid in actuator...
So it doesn't have to be a pressure tank. Remember, the water system is pressurized.
Water arrives under pressure. Were you to store it in an open tank at ground level, you'd throw that energy away, Then later you'd have to pump the water back up to pressure in order to inject it into the...