Sunday, July 20, 2008

On Being Bent and Dissipated (1)

Saturday in Dunedin was cold foggy and drizzling, pretty depressing, so went out to the end of the Otago peninsula with 10 y/o daughter - who always drags me out there (I always end up glad she did) - and 16 y/o son (intellectually disabled, and an eating machine). We lease a crib.

Saturday in Otakou was also cold, foggy and drizzling - actually even worse as always is out there in any weather that's vaguely northerly or easterly. But as I mentioned - we were at the *end* of the Otago peninsula, so there was nowhere further to go so we stayed there.

Sunday (today) was a bit better - not much sun , but no wind at least and fog and drizzle lifted. We did some fishing (no bites) and mucked around and it sort of got me out of my rut as it always does , even though you don't think its going to before you set out - there's nothing all that flash out there that's going to explode you out of your rut, but still it somehow eases you out by next morning. So I'm always glad she drags me out.

And there's always some micro-interesting thing out there if you keep your eyes open. Like today I was thinking about how the motorbike zooming up and down the Aramoana beach - miles away over the other side of the harbour - sounded so close , as though up and down the road outside, and thinking how I'd noticed that effect the odd time before, and how what it probably is is : maybe it just happens when the harbour is quite glassy as today - smooth enough so that the sound waves are reflected coherently off the water surface - so the sound energy is only attenuating in our direction at half the rate that it normally does (though still as the second power , but with a halved constant of proportionality) - and how therefore the effect will not occur when the sea is rough as the complicated surface will just dissipate the energy incoherently.....but when the sea is rough there is also a wind so that would obscure both the effect and one's reasoning about it....I'll have to test this theory out some more.

(So tonight I asked Google to explain this to me , and there is an article about sound carrying over lakes ( ) that suggests, rather , that the main reason is the bending of sound waves by a temperature inversion. Now, it so happens that there was indeed a temperature inversion today - you could clearly sea the smoke from chimneys collecting under a layer about 300 or so feet high. Sound travels faster in the warmer air above an inversion - and this would indeed bend sound back down - as the wave fronts angle obliquely into the inversion, the top of the waves hit the warmer layer first and are sped up - so the entire wave is steered downwards a bit - like the way the outer wheel in a turn has to go faster than the inner wheel, and turns the whole system towards the slower wheel.

Of course any time the sea is smooth, then there is no wind which is rather conducive to temperature layers developing so the possible causes confound each other.

And it seems like both could be correct since they are both variations on the same theme - refraction/reflection of sound when entering a less/more dense medium - perhaps the distinctive effect today was because both were in operation - canyoning the sound out through a layer between the water surface and the inversion, so that the rate of attenuation was even less then half, since the energy was only spreading out in two dimensions rather than three - so that in fact the rate of attenuation would have been more nearly proportional to the inverse first power of distance, rather than the inverse second power of distance.

Some experimentation is needed I guess - electronic send and receive over the surface of a pond, and the same distance apart over grass, and measure it.

But then later I thought of another couple of explanations. Firstly - there are some steep cliffs behind Aramoana so there was probably some echoing of the sound back off those and out over the harbour to Otakou.

Then secondly I got to thinking about the possibility of a wake effect - though really this should only happen (I think) if the motorbike is going faster than the speed of sound ! You drop a pebble in a pond and the waves spread out and attenuate as they go , because the energy is tansferred from a 0-D point, to the 1-D concentric growing circular wave front, and so a fixed amount of energy transferred to an ever growing circle, means the energy density - i.e. the wave - must attenuate. But say now you have a boat speeding through the pond - this is like dropping "continous" pebbles in a straight line. Now the energy is being transferred from a 1-D line (the speeding boat) to the a 1-D line - the wake on each side - a wake is a straight travelling wave. These wake waves do not need to attenuate on energy density grounds , since energy is being transferred from a 1-D line - the boat (or continously dropping pebble) , to 2 other 1-D lines of the same measure - the wakes (though will attenuate due to friction effects).

(I remember flying into Sydney once , looking down while still over the sea and being intrigued by these two long straight ribboned wakes left behind by a ship (or ferry or launch , I can't remember) - that seemed to just persist, travelling on over the sea long after the boat had passed. I say "ribboned" because, although they were straight, they were made of a series of sub-wavelets like

(I guess you can construct a wake mathematically by superposing the continuously infinite series of growing circular wave fronts generated by the passage of the boat - I guess interference effects result in the linear wake).

So I got to thinking - is there maybe a similar wake effect when you have sound coming from something like a motorbike speeding in a straight line along a beach like that ? - the bike is not fast enough to have a trailing wake (thats I guess what a sonic boom is !) - but maybe the energy is still transferred via a linear sound wave front that does not attenuate due to energy density considerations - as would be the case for a noise source at a single point in time.

So if you're ever out at Otakou and the harbour is glassy smooth - which is quite often - and can be all day in winter but usually only in the morning in summer - see if you notice the sound carrying ! - and see if its getting quieter as the second power of distance or as the first power of distance, or some power in between ! And how it is affected by whether the noise source is either continous and moving, or a single point in time and stationary.

Reading an interesting book by Anatole Abragam , a physicist , "Time Reversal" , at the moment - an autobiography, was born in 1914 and came of age during the second world war (I think he is still alive) that kind of got me in the mood for thinking about things like that. He has some very wise things to say about life as well as science. On the other hand, he's a bit of a sexist (I realised on second thoughts), and it got a bit boring towards the end and a bit too much name dropping and general bragging. But heck who am I to criticise !

(How do we know of a statement about life that it is a wise statement !? If we already knew it to be true it is unlikely to strike us as wise as we already knew it. On the other hand it must be something we believe to be true - for a statement to be wise , it must be true - or at least , we must believe it to be true.

So - on what evidence do we judge the truth or otherwise of a statement purporting to be a wise statement ? - since these generally do not come with any lengthy appendices offering empirical data as evidence.

I think a statement that strikes us as wise, is probably usually a statement that we have accumulated some evidence for ourselves , but which we have not yet formulated
any statement about - so that when we see the statement written down we are immediately able to corroborate it by referring to our own experience and memories.

This implies it is impossible to recognise wise statements about life as being such, until we have accumulated sufficient experience to be able to corroborate them as being true - until then , they will probably mean little to us as we will not have any rational basis on which to judge their truth value.

This does seem about how things go - and that it is perfectly rational for youth to ignore the wisdom of age. And also that , unfortunately, wise statements about life are often of little use - since we can only evaluate their wisdom when it is too late. Again - this does seem to be how things go)

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