studiot

Yes and No it is not normally called a sub harmonic, but it could be. Like the louspeaker, the Helmholtz resonator is complicated (although not as much as the loudspeaker since there is no electric to mechanical energy conversion stage). The key word is resonator. You can excite an oscillator with any of the harmonics of its fundamental frequency. So with respect to the resonant (fundamental) frequency of oscillation of the air inside the bottle the effect works best (is at its most efficient) when the rush of passing air contains harmonics of the resonant frequency of the bottle. This is easy to achieve since the passing air approximates to white noise which contains all frequencies. So the bottle 'picks out' or selects energy at is resonant frequency. Incidentally, I don't know how much you understand about the mechanical mechanism of the action but the whole of the air in the bottle does not resonate. A plug of air in the neck is bounced up and down between the pressure of the passing air stream and the restoring force due to the springiness of the air in the large volume of the body of the bottle. This plug of air thus acts as a piston like a loudspeaker cone. It is this that generates the tone you can here, transferred to the general air in the room.

Remember also that we are used to seeing 2D curves on flat paper when we talk about curvature. In that case there is only one direction available to curve in and only one plane for the radius of curvature. When we go to 3D, there are two possible radii of curvature at any point on a curve and if we go to 4D spacetime then there are three, with time as one of the plane's axes. This is really the province of differential geometry in higher dimensions, which I think is ajb's speciality.

Subharmonics are indeed integral fractions of the fundamental frequency in acoustics. There is no magic in this. Acoustic sources are intended to produce a particular frequency (or several frequencies). We call this the fundamental frequency. Each musical note has one fundamental frequency which is the same for all instruments that produce it. However All sources also create distortion due to their particular method of producing the sound. For scientific purposes we want that distortion to be as little as possible For musical purposes it is that 'distortion' or colouring of the sound that leads to the individual characteristic of instruments. The most common form of distortion is harmonic distortion where integral (whole number) and or reciprocal integral multiples of the fundamental frequenciy are mixed in with the fundamental sound. Integral multiples are called harmonics and reciprocal integral multiples are called sub harmonics. Normally it is only the multiples or harmonics that are wanted. These can appear in significant proportions of the overall output sound, although for most instruments the fundamental is still the largest component. Some wind instruments can be 'overblown' and the output sound is largely a harmonic. A physics way of looking at the fundamental is to consider a stringed instrument. Sound sources vibrate as stationary or standing waves, so they have nodes and antinodes. If you think about it the ends of the string are fixed so they must be nodes. You cannot fit part of a wave between the fixing points there must be a whole number of half cycles between the fixing nodes. (half cycles because a node is a zero crossing point and it is half a cycle betwen these in a wave). The smallest number of half cycles is obviously 1 This is the fundamental. You can have as many larger integral numbers of 'wiggles' as you like, jus so long as you have a node at each end. These are the harmonics. but You cannot produce a wave with a lower frequency on its own because there would not be a node at each end of the string. So sub harmonics can only appear as a distortion of the fundamental or higher (harmonic) frequency. I gather you have posted this question in a proper scientific forum, in search of better information than provided elsewhere. That is sensible and you have come to the right place. But the spirit of this (and many other) forums is that the discussion and information is for all to share so should be put into the thread, not some other way. Technically harmonics or harmonic functions are solutions of Laplaces Equation, which does not contain a forcing term. This includes sub harmonics, the fundamental and harmonics. The theory of this is called potential theory. Harmonics are specified in terms of frequency. Physically the lower the frequency the longer the wavelength, which is the amount of distance you need to accomodate (fit in) the wave. The largest physical dimension (eg the length of my string) provides the largest wavelength and thus the lower limit of pure tone frequency that can be generated by a system (rather as Strange said). So, although they may exist mathematically, you cannot generate pure tones lower than the fundamental. However as I noted in post#3 they may be present as distortion to a higher frequency, fundamental or overtone. However loudspeakers are considerably more complicatated than this. A further complication, often ignored in heated loudspeaker discussions, is "Will the soundwave at the frequency considered fit into the room or is it too large?" All too often 'experts' argue about a wave that could never be developed in the listening room. This is of course why concert halls always sound different from your lounge at home. They are much larger so can accomodate longer wavelength, lower frequencies sound waves. Please address further questions within the thread.

Fine, I didn't actually say I agreed or otherwise. That quote was from the contibution to the book by one time particle physicist John Polkinghorne KBE, the quote started his analysis of the flow statement, in relation to the block universe (which I also linked to) which mirrors that here between Lizzie L and the hard physicists here. Pretty well all aspects and all theories of the subject as discussed in this book by the range of experts indicated, including the originator of the light cone. The other quote was from the objectives of the book. It was all supplied in the spirit of adding informatuion for those who might wish to follow it up.

The so called 'block universe' is only one view or aspect of time I think the OOP and Lizzie L are trying to reconcile various views or aspects. Insisting upon one over all others is counterproductive IMHO. After all it was a great day for science when inertial mass was shown to be equivalent to gravitational mass. as was the day when the mechanical equivalent of heat was determined. That's progress. https://www.google.co.uk/#q=block+universe

Like I said no classification scheme is perfect. Peace and harmony certainly exist in concept , but sadly how much exist in reality is another matter.

It won't. I thought you asked for an insulator. Mica is also fireproof.

Dekan, have your heard of the terms abstract and concrete nouns? The moon is a concrete noun - it is made of 'stuff' Love is an abstact noun. They are often concepts. If you wish to deny love then there are plenty more eg anger, sorrow and so on that you cannot. It is a philosophical question as to whether something that consists of nothing itself but supports the existence of concrete nouns (space and time) is itself abstact or concrete. No classification scheme is perfect.

Double spaced Mica sheet should help here.

I'm sorry your Stewart is very different from mine, but someone else may have it. Anyway I meant to say you should try sketching this curve. Have you done any curve sketching? Since you have the ratio of two quadratics consider [math]y = \frac{{a{x^2} + bx + c}}{{d{x^2} + gx + h}}[/math] You are asked what happens when x=0, so substitute x=0; what does that mean for h? Here are a couple of fractions involving quadratics (they are not correct but to illustrate points. How many times does the curve cross the x axis? What horizontal and vertical asymptotes are there? What happens when x is large and+ve; large and negative? You need to consider what about the constants place the corssings and asymptotes to match your requirements.

Physica's solution. I have cleaned up the background a bit.

Yes I am aware of that and that this is your specialist field. What you are basically saying is the limit of resolution (nothing to do with Heisenberg) is the interval between two zero crossings. We have to assume that time itself flows evenly within this interval. And yes I am using 'tick' in the most general sense. This is somewhat akin to the limit of spatial resolution of various types of microscope.

Will this not also have a vertical asymptote at x = -1? Your curve is stated to have a single vertical asymptote I don't have your version of Stewart, but in my 1987 version he sketches various cases of vert asym. Does he do that in your book and can you find a type with a single v asympt? A chapter/page ref might be useful for others.

I thought that discussion on relativity had been declared off topic by hypervalentiodine, since we are supposed to be discussing time and the OP. The OP had the sense to realise that no one can tell you what time is. He was seeking 'a basic understanding'. Now one thing to understand is about the flow of time. Here is some quotes from the recent Cambridge University book 'On Space and Time', edited by Professor Shahn Majid. Lizzie L I suspect you would find much of interest in this book. Although the book deals also with the possible granularity of space and time, the following is not in the book The issue of time flowing is interesting because of the way we measure it. Does time flow evenly or jerkily? All clocks proceed unevenly, within a tick cycle. Old fashioned chronometers proceeded with a series of small jerks forwards. More modern atomic clocks still run at uneven rates through their tick cycle, this can be modelled by SHM.

Well the 'curvature effect' would be uneven and somewhat reflect the shape of the object. You would, in principle, be able to deduce the shape of the object from the variation in the curvature 'field'. Note the words in inverted commas are meant to be taken in a somewhat colloquial sense rather than a strict physics one. However most objects on a scale sufficiently large to really exert appreciable gravity are roughly round. Even Saturn and its rings could be called round. There are two effects that promote this. Firstly, surface tension tends to create globular shapes as with raindrops. Secondly, extended shapes are subject to quite large disruptive forces due to twisting and rotation. So they tend to break up.

This is a truly personal question since each of us is different so I can't say if my experience would work for you. However here is my truly personal experience. I did more or less what you are suggesting many years ago for my A levels. I rewrote my class notes , along with other material from books, in the way that I understood it and how I understood it all hung together. This involved quite a few drafts and rewrites - be prepared for that. This helped me greatly to consolidate what I knew and cetainly produced favourable results in the A and S levels. One teacher at the time said famously The more times you write it down the more danger there is you will remember it. A parting point, if this is for you own consumption it does not have to be neat copyplate, just readable. That saves quite a bit of effort. go well

Thank you for the solution paper. My only comment is that i is the unit vector so in deriving H you should have brackets round the kx-kl0 thus H = (kx-kl0)i Otherwise you seem to have solved it. Well done. Would you like me to post your solution until you?

If you are going to introduce equations then you should be prepared to answer legitimate questions about them. I am sorry you appear to feel vindictive about this. Surely it is easier to simply state what you think is travelling at a velocity you have granted it. And no, I do not think you invented relativity, nor was I discussing it. The discovery of the Lorenz transformation preceeded Einstinian relativity and was a practical observation that is actually independent of it.

Well it was clearly you who introduced them. In two out of eight equations you have used the symbol v, which you tell me stands for velocity. Why is it so unreasonable to ask what is travelling at this velocity and in what coordinate system?

So getting back to the Lorentz tranformation, You have stated (correctly) that v is velocity, but have not stated what is travelling at this velocity or what frame it is being measured in. Without this information the formulae given cannot be used.

Correct in this case but, Actually you can transform some derived physical quantities into others with suitable processes, eg the Fourier transform, but see here

Since you introduced the equation (by copying someone else) I'm waiting for you to do some actual mathematics. I have asked you at least five times to explain v, which you also introduced. So far you have told me it is superfluous, and ignored every request to explain in full what this variable represents. So, once again, I am asking you to explain yourself. Why for instance introduce v if it is superfluous?

No it just looks like nonsense to me since the terms have not been defined. since you won't do it I will. If your equation is valid it must hold for every value of v : v<c. So I define v=0. Then your equation tells me that x = x Whoopee!!! Not a rotation or other animal in sight.

Perhaps that's because you are not setting out your 'math' correctly or conventionally. Bald statement of equations, without specifying variables and constants constraints and limits of applicability and developing a train of mathematical argument (proof) does not make 'math'. So you are not going to answer my question?

Yes a velocity indeed, but what velocity in what coordinate system? That is the key question. I really don't care or see that it is relevant that some people have invented yet another superfluous new word called rapidity.