SciBlogs

Archive October 2010

A daylight conundrum Marcus Wilson Oct 29

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Our organic alarm clock has now taken to jumping on the bed at about 5 in the morning and purring very loudly in an attempt to persuade us it’s breakfast time. It’s not surprising, since sunrise (and therefore cat-rise, if not Marcus-rise) is becoming earlier and earlier.

Daylight hours are now long – in fact the South Pole is now in non-stop daylight. If you’re there with no cloud present you’d see the sun circle the sky, at fairly low elevation. A horizontal surface would get non-stop daylight, but a vertical surface obviously wouldn’t. About half the time it would be lit, and half the time in shadow, with the sun behind it.

So here’s the brain teaser. In the course of a 24 hour day, is it possible for a vertical wall to be lit for more than 12 hours (clouds and other obstacles not getting in the way, of course)?

And, if so, where in the world would the wall be, what day of the year would it be and what is the maximum time it could spend illuminated?

No prizes, other than a chance to feel smug.

Sound proofing by closing a door Marcus Wilson Oct 27

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We’ve had a couple of fire alarms in the last week. Both false alarms, which is good. We still however pile out onto the grass in front of the Faculty of Science and Engineering and time how long it takes for the fire engines to arrive and bet on whether the Hamilton City-based crew will beat the Chartwell-based crew to the scene.

We have five small buildings joined together - and an alarm in one will trigger the alarms in the other. Yesterday, when the alarms were switched off, the alarms in just one of the buildings carried on for a while. As I walked through that building to get to mine, the noise was pretty intense. But after going through a couple of doors and into my office, I could hardly hear it.

Conclusion: doors make pretty good sound proofing. But why?

Sound moves through air as a compression waves. That means the air molecules move backwards and forwards as the wave passes, causing a fluctuation in pressure. It’s this pressure change that your ear picks up and your brain interprets as sound. Sound also travels through doors as a compression wave. And like all waves, when the medium in travels in changes, there can be reflections.

Light is an obvious example. When light hits glass, some of the light gets reflected. We can see faint reflections, even though most of the light is transmitted through. Just how much light is reflected depends on a quantity called the impedance of the glass. Or, more precisely, the relative difference between the impedance of the two media – the air and the glass.

Similarly, there are acoustic impedances. Where two materials have very different acoustic impedances, there will be a lot of sound reflected, and very little transmitted. Acoustic impedance is strongly related to the density of the medium. A door is way more dense than air, and so most of the power incident on the door will be reflected. Relatively little gets through, and so the noise is much quieter on the other side.

This is one reason why things are typically very quiet underwater even if you are in a noisy swimming pool. The noise from a hundred screaming children travels very nicely in the air, but most gets reflected off the surface of the water and little actually makes it underwater. Also, your ear is designed to hear in air, not water, and so again much of the power hitting your eardrum gets reflected and fails to transmit through to the inner ear.  Everything appears quiet.

It’s the Thesis in Three final tonight – I’m really looking forward to it.

Electrical Noise Marcus Wilson Oct 26

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Lectures have finished; students now are into the exam period; and my thoughts naturally turn to research for the summer. To be more accurate, they first turn to marking the aforementioned exams and other assignments, but research will quickly take over.

One of the projects we have going involves recording small electrical signals from a system in our lab. Small signals for us mean a few millivolts, with very little current. Probably the major problem we face is electrical noise. That means that the signals we want are contiminated by those from other sources – just like it’s hard to hear a bird singing in the garden if you live next to a busy road – the signal from the bird is contaminated by the road noise.

Some sources of electrical noise are unavoidable. Thermal noise (or Johnson noise) is unavoidable, since it comes from the thermal energy of electrons in the system. There are ways of reducing it, such as cooling your apparatus with liquid nitrogen. Shot noise is a different effect and is arises when there are very low currents. Since each electron carries a discrete charge (small, but not infinitessimal), charge doesn’t flow smoothly – and that gives you a fluctuating current.

But the problem we have is contamination from other electrical sources. There is so much electrical equipment around the place that the room is full of alternating electric and magnetic fields. These fields will induce currents to flow in the equipment – e.g. through Faraday’s law – a changing magnetic flux through a loop will induce a voltage around the loop.  Also, any piece of wire can act as an aerial and electrons in it respond to alternating electric fields.

There are simple ways of reducing this effect – e.g. by having your cables nicely shielded but it’s not perfect. Strategically-placed aluminium foil can be a great help sometimes – it cuts out electromagnetic waves because it is so conductive, as you can demonstrate with a mobile phone. Clever routing of the wiring to avoid large-area loops (i.e. reduce the extent to which Faraday’s law can give you voltages you don’t want)  is good practice too.

However, our lab sited next door to the switch room for the whole building (where the mains power comes in to supply most of the Faculty of Science and Engineering) which is hardly ideal, and so we might just have to put up with the problem for a while.

 

Pendulum mayhem Marcus Wilson Oct 22

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One of the main intentions of our 2nd year Experimental Physics paper at the University of Waikato is to have students learn how to put together a physics experiment that measures something, and to measure that thing in a systematic and robust manner. What that means in practice is dealing with uncertainties.  Whereas the average person might want everything to be absolute-without-any-doubt-certain, it is rare that we can be absolutely unequivocal about anything in science. But what we can say, and should say, is exactly how certain we are about something.

In a physics experiment we tend to do the opposite – and speak about how uncertain the final result might be, and what are the main drivers of that uncertainty. A good experiment will be one where thought has been given to where these uncertainties arise, and effort taken to minimize these.

With all this in mind, I had my students perform a small ‘test’ last week. I stuck them in a lab, and told them to make up a pendulum and use it to measure the acceleration due to gravity. On the face of it, this is easy, and if you’ve studied physics at all you might well have done it. The theory states that (for small amplitudes) the period of a pendulum is given by 2 times pi times the square root of (pendulum length divided by the acceleration due to gravity).  So if you know the pendulum length, and measure the time for a swing, you can work out the acceleration due to gravity.

But is it that simple? There are in fact a whole host of problems. What is the pendulum’s length? The mass at the end certainly won’t be a point mass. In fact, a systematic uncertainty in the measurement of length can be accounted for by plotting a graph of period squared against length – the gradient of this line won’t be affected; the systematic uncertainty will simply mean that it won’t go through the origin.

Another uncertainty is the timing of the period.  We could set up laser-gated timing, but stopwatches are easier. There is the issue of whether the pendulum is actually at rest when you release it and start timing – e.g. do you tend to push it along to start with – i.e. it’s not released from rest?  But you can get around that as well, by not starting the stopwatch when you release it; rather waiting for it to do a complete swing first. This also accounts for any systematic uncertainty in pushing the button on the watch – if you tend to be slightly late, you will press it slightly late at the start, AND slightly late at the finish, and the two effects will cancel. The time on the clock will be correct. Additionally, timing lots and lots of swings is much better than one; the uncertainty in time is reduced when we divide it by 100 swings.

What is a small angle? How secure is the pivot – i.e. does the effective length vary in the course of a swing. Moreover, does the pendulum stay the same length throughout? We used a mass on a string, and the string might easily stretch throughout the experiment.

These are just some of the things that students had to think of when doing their experiment, which is rather harder than it might appear.

After the ‘test’, I had a go myself, trying to take into account all these issues and more. I used the same equipment as the students – string, stopwatch, small masses, a retort stand – and tried to get the best measurement I could. It’s a tough one. 

My measurement, for the record, is not as certain as I would like. I’ve measured the acceleration due to gravity, in our lab, as 9.87 metres per second squared, with an uncertainty of 0.10 metres per second squared. I reckon, after working through it, it’s a tough ask to get that uncertainty much lower. But if you want to give it a shot, please do and let us know how you get on.

 

Sticky Milk Powder Marcus Wilson Oct 21

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Earlier this week, we had the end-of-year display of student engineering projects. There were lots of posters put up to browse around over tea, several interesting large objects such as pieces of electric cars, and many fascinating talks given by the students.

One of the most enjoyable talks was given by student Timothy Walmsley, concerning a study on the sticking of milk powder in spray dryers. To convert milk into powder form it is sprayed into a dryer; the milk solids remain and fall to the bottom but the water content is removed; the result is something that is easily packaged and transported.

However, there’s a bit of a problem. Anyone who uses milk powder at home will have realised it’s sticky. I think it’s horrible stuff – it gets itself all over the place, then you can’t get rid of it. I learned on Tuesday that sticky milk powder is one ‘phase’ of powder – there is also a non-sticky phase, and there is a phase transition that separates the two. (Just like ice and water are two different phases of water – and there is a freezing/melting transition between the two.) If the temperature is high enough milk powder isn’t sticky, but if it drops too much we can expect the sticky form. Just what this temperature is depends on other conditions, such as relative humidity, but we are talking something vaguely around 70 Celcuis. Timothy has done a nice series of experiments studying this sticky transition and thinking about its application to what goes on inside a dryer.

Here’s an example of the issue – as I understood from the talk, the exhaust air exits at about 80 degrees Celcius. That’s warm, and there’s a lot of energy that is going to waste here. Why can’t we recover some of it?

The problem is that a little bit of milk powder finds its way into the exhaust. If we take heat from the exhaust (e.g. with a simple heat exchanger) we cool the exhaust, and we get into the non-sticky-to-sticky phase transition territory. That means that the particles of powder would start sticking onto the inside of the exhaust pipe (or so I understood) which would cause problems. It’s a bit like the problem with ice forming in the outside unit of your heat pump in cold weather – the pump has to enter a defrost phase to get rid of it – and in the spray dryer exhaust pipe something similar might have to happen if heat is to be recovered from it.

Overall, a fascinating talk about a phase transition that I wasn’t aware of.

 

 

The3is in Three is Back Marcus Wilson Oct 20

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October is ’Postgraduate Studies Month’ here at the University of Waikato, and the highlight is ‘The3is in Three’.I talked about it last year – it’s a competition in which PhD students have to explain their research in three minutes using just one powerpoint slide.

This year two of my PhD students have done very well. One has got to the final, the other was one of two ‘highly commendeds’ who didn’t quite make the final. As a supervisor of a finalist, I get ‘VIP’ tickets to the final (I’m not sure what a VIP ticket entitles me to, since the event is free to the public), which is next Wednesday. I am absolutely sure it will be another fantastic event.

Te Radar is back as compere, though this time we are moving out of the university into Clarence Street Theatre in central Hamilton.  7pm start, Wednesday 27 October, and it’s absolutely free. Come and enjoy the show.

And this time I hope a science student wins it.

Diffraction Marcus Wilson Oct 18

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If you’re like me, you’ve been mesmerized by the colours created by reflections from a DVD or CD. The discs do a great job of splitting the illuminating ‘white’ light of your home light-bulbs into its constituent colours. But unlike a prism or raindrop, which achieve this effect through refraction (blue light travels more slowly than red through glass, which causes the white light to separate out when it is incident on glass from air), in this case diffraction is the key physical effect.

Diffraction is a property of waves. Water waves diffract, sound waves diffract (this is why, to a large extent, you can ‘hear’ round corners) and light waves diffract. However, with the first two, wavelengths are long (of the order of metres) whereas for light, wavelengths are a bit less than a micrometre (thousandth of a millimetre) in size, and that makes the effects hard to see in everyday life.

Those of you at school will learn about diffraction gratings. Here, you stop the passage of light except for very narrow strips, a fixed distance apart. The result is diffraction – the strips each radiate light, and the waves from each source now interfere. If a peak from one slit always arrives with a peak from another slit, you get constructive interference, and a strong signal (bright light). But if a peak from the wave from one slit arrives at the same momement as a trough from a wave from another, you get destructive interference, and see nothing.

A similar thing happens with reflections from the surface of the DVD. In this case, the DVD has small pits in the surface, about a micrometre in size. This causes strong diffraction of light. But the angles at which you get constructive interference depends on the light’s wavelength, and therefore its colour. Red light, being the longer wavelength, will be diffracted more strongly than blue, and so we see the colours separate out. The effect is a shimmering rainbow of colours on the back of the DVD, thought the mechanism is very different from that which causes the rainbow in the sky.

There’s a nice demo of diffraction with sound at http://phet.colorado.edu/en/simulation/sound  – put up two sound sources and move the listener around to hear the effects of constructive and destructive interference.

There’s also some nice wave effects you can see on Google Earth along the coast near Raglan, though there is some complication with other effects, such as refraction of the wave in shallow water.

 

Maths and Physics Marcus Wilson Oct 14

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I had this lovely piece of written feedback in an email from a student yesterday.

I … think your emphasis on the physics rather than the math that describes it … is really good, my problem solving approach has changed from wondering what equations I have at my disposal to what’s actually going on.  
 
What this student has hit upon is that maths can get in the way of physics. I think I’ve said it before, but I’ve found there are two common reactions students have to physics equations.
 
 First, those who like maths (like the above student) go straight to the equations, and so can miss the point. Rearranging equations is easy if you like that kind of thing, but what does it tell you about the physics? It’s the ‘mapping-mathematics-to-meaning’ game of Tuminaro and Redish (Physical Review Special Topics – Physics Education Research, 3, 020101 (2007)). But the key step in this game is to interpret what the maths is telling you about the physics. That is not always done.
 
 The second reaction is the opposite – to see the maths and switch off, because it looks complicated. That doesn’t help either.
 
I have wondered whether I should experiment next year by taking a paper I teach (or part of a paper) and removing the maths entirely. Don’t have a single equation. What happens to the students’ ability to apply physics? Methinks there could be some opposition to this, which is why I would probably try it on just part of a paper to start with. Then, once the students understand what is going on, I can try re-introducing the equations.
 
Do I dare try it?

Dealing with random things Marcus Wilson Oct 12

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In physics, just like elsewhere in life, there can be more than one way to tackle a problem. An example I’ve been thinking about recently is in the computer modelling of random processes (which is essentially what my research is about). Rather than talk about neurons and what causes them to fire or not-to-fire, I’ll draw on a more well-known example, the drunkard’s walk.

I’m not sure who coined the phrase, and whether the term ‘drunkard’ refers to any particular physicist, but in simple terms the process is this: 

A physicist emerges from a bar late at night and has absolutely no idea which way home is. Every step he takes is in a completely random direction, and each step is uncorrelated with the previous one. (In other words, he forgets which way he was travelling in after every step.)  Where does he end up after ten minutes (assuming he is still on his feet)?

Of course, we don’t know the answer to this question – his movements are random – but we can say some things about his movement. First of all, on average, he will go no-where. He is just as likely to take a step northwards as southwards, so the mean position will be at the door of the bar. We could run a computer model here. Start lots of physicists at the door of the bar, and, at each time step, move each one, independently, either a step northwards or a step southwards. After several time steps, look where they are, on average. The centre of their distribution will be at the starting point.  BUT, the average distance of a physicist from the door will increase as time increases (that is, the distribution of the physicists spreads out). It can be shown (as Einstein did for Brownian Motion)  that the distance increases in proportion to the square root of time. If you quadruple the number of steps, the average distance from the door will double.

That’s a simple example, and realistic ones are more compllicated, usually with the motion being partly deterministic, or each step not being uncorrelated with the previous. But similar ideas apply. Buried in the above paragraph, I’ve hinted at two different approaches for considering this problem. One is simulating lots of examples – i.e. write down an equation of motion for a physicist, and simulate it on the computer lots of times.  For such a walk, this would be an example of a Langevin equation, after Paul Langevin, who studied Brownian Motion. (Technically, that’s not quite true, because the random part isn’t gaussian, but we could formulate the problem so it is, but that’s harder to describe.)

The other is considering the distribution of probability. Instead of writing down an equation for each physicist, we construct an equation for the probability of finding a physicist at a given point in space, and describe how that probability changes with time. This is called the Fokker-Planck equation. The two equations are equivalent descriptions of the same thing – from the Langevin equation you can i derive the Fokker-Planck equation. Which you choose to work with depends a bit on what you are trying to do.

So we have the same process, but we can use either method to describe it. That’s quite often the case in physics. Another nice example is the equivalence between Schroedinger’s equation and the Feynman path integral in quantum mechanics, but I’ll leave that to another blog entry.

 

Scholarship exams – answer the question Marcus Wilson Oct 09

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Last Saturday I did a morning session with high-school students who are preparing to sit the NZQA scholarship exam in physics later this year. This exam is aimed at the top students in any year group – with an aim of rewarding them and recognizing excellence.

The questions are certainly hard – and to do well a student needs to have both a broad and deep grasp of the physics he or she learns at school, AND the ability to apply it to situations they haven’t seen before. (If you’re interested, you can download  last year’s exam from here.) This latter attribute leads to some nasty-looking questions. The first part of approaching a question is therefore always working out what kind of physics applies and what the examiners are wanting you to show/explain/derive etc.

I’ve been through the feedback I got from students after Saturday’s event. The most common theme was asking me to provide free food, which is duly noted for next year, though whether my head of department will agree to it is another question. However, one of the physics-oriented comments was suggesting I spend less time on how to work out what the question is about, and more on details.  I’m sorry, but I shall answer no to this one, for the following reason.

The examiners’ reports over several years have emphasized that students have struggled to interpret the question. Without fail, it appears on the list of attributes demonstrated by unsuccessful students, year after year. Whereas, for the successful students, examiners routinely comment that the students are able to apply physics in novel situations.  And that’s part of what scholarship is about. It’s also part of what working with physics in a research career is about. Research isn’t about applying physics to text-book situations, rather, about using it in ways that haven’t been done before.

So, I make no apology for trying to help students to identify the key physics happening in different situations. It will stay in my scholarship-preparation presentation until such time that the examiners stop talking about it in their reports. 

Related to that is simply reading the question properly. That’s true for any exam – if you don’t answer the question that has been asked, then don’t expect to do well in it. It’s one of the biggest single cause of losing marks in exams, and so is probably the best single piece of advice I can give. It would be good to pay attention to it.

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