Thursday, April 26, 2007

The Greenhouse Effect

In conjunction with the recently concluded Earth Week, let's take a physics look at the Greenhouse Effect.

The Greenhouse Effect doesn't only occur on Earth: it is a phenomenon that is present on both Venus and Mars. It is a purely natural effect first studied in detail by a scientist named Svante Arrhenius. If you remember your chemistry, this fellow also provided us with our theory of acids and bases: acids are substances that donate H+ ions, bases are substances that donate OH- ions. Sounds familiar?

Certain kinds of gas molecules, such as water, carbon dioxide and methane, are very adept at absorbing infrared radiation, more so than other kinds of gas molecules. Simply speaking, these gas molecules are able to absorb infrared radiation and start vibrating, whereas others like oxygen and nitrogen, dislike infrared radiation, because they don't really have any way of properly dealing with the energy if they absorb it.

In a planet completely devoid of an atmosphere, the ground absorbs solar radiation and heats up. Remember I mentioned about how every object gives off infrared radiation? At the same time that the ground is absorbing radiation from the sun, the ground is also giving off its own infrared radiation. As the ground gets hotter and hotter, the amount of infrared radiation it emits gets more and more too.

Eventually, it will reach a stage where everything is nice and balanced: the amount of solar radiation absorbed is equal to the amount of infrared radiation emitted, and the ground will remain at a constant temperature thereafter. It turns out that without the atmosphere, the surface temperature of the Earth would be 25 degrees celsius lesser than what it is now. Think of the temperature of Singapore being 0 degrees celsius!!

The thing that comes to our rescue (indeed, the thing that allows life to thrive on Earth) is our atmosphere. Our atmosphere actually acts like a blanket, with the greenhouse gases like water, carbon dioxide and methane absorbing the infrared radiation emitted by the ground that would have gone into outer space, and then re-emits it back to the ground.

This means that on top of the solar energy incident on the Earth, there is also a significant amount of energy being emitted by the atmosphere back to the ground, causing the temperature of the ground to rise to a much higher temperature than expected.

Of course you would already know that the level of carbon dioxide and water is controlled by the carbon cycle and the water cycle respectively. The gist of it is that carbon dioxide is mainly gotten rid of by photosynthesis, and water basically gets rid of itself by precipitation. These cycles maintain a fine balance, and are now unable to keep up with the growing levels of carbon dioxide being emitted by burning fossil fuels.

The increase in greenhouse gases necessarily means more radiation being returned to the ground, which means that the ground gets heated up more, leading to higher global temperatures, or global warming.

This I guess you should already know, but something of greater interest is what we know as the runaway greenhouse effect. The atmosphere of Venus comprises mainly carbon dioxide, which leads to a huge greenhouse effect on the planet. The surface temperatures are estimated to be about 500 degrees celsius (high enough to melt lead and zinc), which is higher than that of Mercury's surface temperature despite being so much further away from the Sun. The greenhouse effect also causes the day and night temperature of Venus to be of no significant difference, despite the fact that a Venusian night lasts about 116.75 Earth days, giving it a long time facing away from the Sun.

It has been theorised that Venus once had water on the surface, much like Earth does today. But water is a greenhouse gas, and somehow Venus was hot enough such that quite a bit of the water on the surface evaporated over time. Since water accelerates the greenhouse effect, the temperature of the surface of Venus must have risen, which caused more water to evaporate, which in turn causes the temperature to rise further, and... you get the point. This is known as the runaway greenhouse effect, and the end result is a planet that would immediately incinerate most living organisms.

Some trivia about the greenhouse effect: one of the most important contributions to the greenhouse effect on Earth is the methane gas, which is given out by cows when they fart. So, it's not all about carbon dioxide from fossil fuels!

Another thing: the name greenhouse effect is quite a misnomer. Greenhouses work by allowing light to pass through the glass, heating the ground. The ground then heats the air above it, which rises up, but is unable to escape from the greenhouse because of the roof, of course. It's pretty much like boiling water while keeping the lid on.

Another fine example of scientists naming things poorly.

Friday, April 20, 2007

The Elusive Photon

I'm sure most of you have heard some of your classmates mention "photons" in class, or at least people mentioning how light is also a particle, and also see me ignoring them.

So here I will address the question: what is a photon?

First of all, the reason why we know so clearly that light is a wave arises from this wonderful ingenious experiment (I might have mentioned this in class) known as the Young's Double Slit Experiment. I won't go into the details of the experiment, but you can check it out yourself here. But what the experiment demonstrates very clearly is that light undergoes a process known as (you can check it out too)interference. This process is one very special phenomenon associated with waves, much like reflection and refraction are special phenomenon associated with waves.

So a whole generation of physicists studied electromagnetic waves and made many conclusions about how electromagnetic waves should behave, and sure enough almost all phenomena associated with light could be easily explained by the fact that light is a wave.

One would think that the answer is immediately apparent from the experiments: light is a wave, and no more arguments. But there were a set of three physics problems at the beginning of the 20th century that were thought to be minor issues at that time. They defied the physicists' attempts at explanation.

One of them was known affectionately (or rather unaffectionately) as the ultraviolet catastrophe. A simplified version of the problem goes like this: when light was assumed to be an electromagnetic wave, it was predicted that if a person stands in front of a stove, he would be exposed to an infinite amount of radiation, and would therefore instantly burn to death, which is of course not true! Such a gross error definitely needed prompt correction.

The other two problems are the famous Photoelectric Effect and the less famous Compton Effect . In both cases, simply ignore the math.

All three of the problems had one thing in common: they could all be solved if we allow ourselves to envision light existing as billiard ball-like entities. Don't concern yourself with the technical details here, unless you are willing to crack your heads, but these three problems were all resolved by assuming that light existed in little chunks at a time called quanta (hence quantum physics). You can think of it as the light ray being composed of billions and billions of microscopic particles called photons.

What's the difficulty here? Well, fundamentally particles and waves are really different. For one thing, in a wave, the energy is continuous throughout the wave. When you shine light on a surface, the energy arriving from the light will gradually accumulate on the surface, and heat it up. But if you think of light as little billiard balls, then energy transfer comes in short "spurts": when a billiard ball hits the surface, the energy is immediate transferred to the surface, so there is a sudden "spike" in the total energy of the surface.

What is even more troubling is the fact that waves undergo refraction and interference, whereas particles absolutely do not. How can we explain the wave-like properties of light if we treat them as particles? On the other hand, how do we explain the three problems without resorting to particle-like properties?

The problem gets even worse!

After awhile, physicists were actually able to detect wave-like properties in electrons, which we definitely thought were particles. They were able to perform Young's double slit experiments on electrons, and showed that electrons can behave as waves too! How can that be?

A French prince named Louis de Broglie came up with a most proposterous suggestion, that turned out to be right. He suggested that everything in the world had two "faces": wave-like behaviour, and particle-like behaviour. And he really meant everything.

So even you can behave like a wave, undergo interference and all, but because of your incredibly great mass (in comparison to the electron, for example) the wave-like properties are not detectable, and the particle-like properties dominate.

It may not sound sensible at all, but if you read more about this incredible theory and its history and how the ideas behind quantum physics first developed, you would see that we were forced into a corner, and were basically forced to concede something that makes little common sense, but yet was right, because that was what the experiments were saying.

How can something be both particle and a wave? The modern understanding, is seriously mind-blowing. I don't truly understand it on some level, but what I understand is this:

Before you observe anything, you will know absolutely nothing about that thing, and so you will never know whether something is a particle or a wave until you decide to look at it. Now, in order to find out if something is a wave or a particle, we must make an observation, which involves some kind of measurement. It turns out that depending on what we choose to measure and what the experiment set up is, you will get different conclusions! If you design an experiment to measure the wave-like properties of something, you will detect its wave-like properties. If you design an experiment to measure the particle-like properties of something, you will detect its particle-like properties!

Sounds silly right. But it is a lot more ingenious and subtle than it sounds. On top of that, it works pretty damn well too.

An excellent example of this idea would be the extremely famous Schrodinger's Cat . You can read it yourself here, or click on the external links: there are some that give a very quick introduction.

For those who are interested in pursuing this further, you can check out the book "Who's Afraid of Schrodinger's Cat?", or the comic-like book "Introduction to Quantum Physics": the series with introductions to a lot of different subjects in comic form.

Like in all things complicated in physics, skip the math. It can wait. You can still understand most of this stuff at a basic level if you read the right stuff!

The School Next Door

Okay, today let's take a break from physics. As you can imagine, I'm sitting here in the staff room staring at your practical worksheets and have decided not to mark them for the time being: the task is too daunting. And I'm sick of preparing for your lessons as well. Teachers need breaks too.

My time in RI was definitely the best period of my life, better than the time spent in RJC, and definitely definitely much better than time spent in NS. You will find that the friends that you make here in RI will last for a very long time, typically longer than the friends you will make in RJC. These are the people you grow up with, and the RI crowd tends to be a very weird crowd. JC is all about being "normal", being part of the mainstream culture, whereas in RI differences are very much more acceptable.

In JC you get to drop the subjects you dislike, although you must be very wary because many subjects morph into monsters. I took physics, chemistry, mathematics and further mathematics, and even though I did well, I still hate chemistry to this day. Chemistry and biology are two subjects that will rear their ugly heads over in JC, although I can see that the current Raffles Programme chemistry and biology are already gearing you towards JC style chem and bio.

Subjects like economics were very popular in my time, and is now incredibly popular, with virtually everyone taking it as their humanities, but I can't say too much about it, other than the fact that it does seem rather interesting if you are interested in all that.

As to physics and mathematics, there shouldn't be much problem. Physics is really quite manageable, because they can't push the standards up too high without bringing in higher level mathematics. Mathematics will be built on what you already know, plus some more stuff that are rather interesting, but really quite manageable. Further mathematics is problematic, but since they took that out, you don't really have to worry.

There used to be this thing called Special Papers in my time. I took two, in physics and mathematics. Nowadays, they call them H3 subjects, and from what I'm hearing many people are taking them in either math or physics. I'm not too clear on what this is really about, but special paper is just harder questions set to test your math and physics abilities in a more stringent manner, with physics incorporating some calculus (although almost every student manages to skip through this part by not answering those questions).

You will encounter really irritating subjects, like General Paper, the most useless and pretentious thing in the world. I still don't understand how they expect any of us to write anything sensible for their essays, because very often the problems that they are discussing are so complex, and so multi-dimensional that it is impossible to say anything smart about it without some good hard evidence and at least 200 pages of explanation and report.

Project work is hell. Completely pointless. You'll see what I mean. Good luck for that.

School wise, you will have to start taking your own notes, which is what I've been telling you people in class during lectures. Some periods will be lectures, where you will go to the lecture theatre and listen to the tutor teach about the topic in the subject, while others will be designated tutorials, where you will go to classrooms and discuss the questions set in the tutorials with your tutor. Nothing very new here, except that the stuff that you learn isn't going to come from the classroom, but from the lecture theatre. What you learn during the lecture is entirely up to you, and sometimes even if you don't turn up (which is illegal, of course, but I don't pretend to being an angelic student back then) they don't really care.

To tell you honestly, I used to skip school, skip classes, especially S-paper classes. But one thing that I never skipped was chemistry, because that was my worst subject. I was, and still am terrible at chemistry practical, and so those practical lessons I would definitely go. But physics and mathematics, especially S-paper, were really useless lessons.

In all, academically you are pretty much on your own. You have to learn the skills of studying by yourself to some extent, without the help of teachers to spoon-feed you notes and all, and definitely you will need to discipline yourself. You can choose not to do any of your tutorials, which is precisely what I did for physics, but at the end of the day you must get your grade.

Socially, JC is more geared towards being "cool". Although I know it sounds very silly, but that in fact is what it is. There are set behaviours and things to say that are considered normal by each class, and if you don't happen to be that particular thing, then you won't fit in. I didn't like my class, to tell you the truth, and I don't think they really liked me as well, but we were really different people. Thank god for RI friends and CCA.

Of course there's also the matter of there being girls in RJC, and well, okay, that's nice and all. But a word of advice, stay away from all those till after your NS, because I think no one is able to emotionally handle any relationship properly at that age, and under those circumstances. You know too little. I know it sounds kind of weird coming from me, and I still can remember how I resented the way other people say things like that, but once you get through NS, you will see what I mean.

Teachers, well, you won't be as close to them as you are to some of your teachers now. My class was very close to my RI teachers, and even up till now they still invite us over for Chinese New Year, or we have dinner together or something. When I came back to RI to teach after 5 years away from this school, all my old teachers could still remember my name, and other weird details associated with me. They are amazing. In RJC, you can't expect this level of closeness, because very often they spend too little time with you, and in that short window of time that they are talking to you, they are talking business.

Things are different over there, and I think some of you will adapt really well to the environment, while others will probably not. When it comes, don't be too sad if you're not "in", because there are many people out there who are like you. I think what is most frustrating about being in RJC is that people tend to forget the true purpose of being in school, which is to learn. I hope throughout the course of the time you are spending in RI you will appreciate how amazing knowledge in any field is, not only physics, and not forget that when you go to RJC, and not finish the JC course feeling uninspired and unsure of what you want to do with your life.

Because JC is the period of time that shapes your ambition and the future "you". Participate actively in CCAs (there were months when I never reached home before 8, and would lose every single Saturday to CCAs) and pursue your academics and everything else with passion. Don't get too caught up with the glamour and girls and fun associated with JC, all the socialising and going out and parties, because those are empty things in the end.

In the mean time, enjoy your time in RI. It probably doesn't get any better in the next 5 years!

Tuesday, April 17, 2007

Resonance

Quick review:
Frequency: number of oscillations per second.
Period: time taken for one oscillation.
Amplitude: maximum displacement from equilibrium position (rest position) of the particle or pendulum.

We've all heard urban legends of people being able to break glass, or more usually crystal by singing at high pitches. Some of you would probably also have seen this picture:




This is the famous Tacoma Narrows Bridge just before its collapse, which started tilting left and right on a particularly windy day. If you can find the video clips detailing the collapse, it's quite amazing.


All of these phenomena, and much more, can be attributed to the natural phenomenon of resonance. So what exactly is resonance?


Every object, when excited in some way, vibrates at a very special frequency known as its natural frequency. For example, in the lab experiment you just did with the pendulum, the pendulum has a natural frequency that can be calculated. Those of you who still haven't handed up you lab report, you can verify that this formula is true:


Where T is the period of the pendulum, pi is just pi, l is the length of the pendulum, and g is the acceleration due to gravity, which is 10 m/s^2.

So a pendulum when set into motion will automatically start moving at this period or frequency called its natural frequency: the frequency at which it oscillates when it is not disturbed by anything. Anything that is able to oscillate has a natural frequency, a kind of preferred frequency at which they like to oscillate.

This also happens when you blow air across a half-filled bottle to produce a sound: this sound has a certain frequency that is the natural frequency of the air inside the half-filled bottle. When you let your arms swing naturally by your sides, they should be swinging near the natural frequency. When you hit a drum, or a string, or when you produce a note on a wind instrument, you are making the skin, string or air vibrate at its natural frequency.

But of course, in a pendulum, I can try to force it to oscillate at a faster or slower frequency by trying to control the motion with my hand: I can grab the string above the pendulum bob and try to make it go faster or slower by moving my hand faster or slower than the natural frequency.

You can try this at home with a broom stick. Grab the top of the broom stick with one hand, and allow it to swing naturally, without you exerting any force. It will start oscillating at its natural frequency. Now, you can try to make it swing faster by applying a force through your hand. Observe what happens to the amplitude of the swing as you try to make it go faster. You should see the amplitude getting smaller and smaller, and the broom swinging less and less.

If you try to make it oscillate really really fast, by moving your hand back and forth really really quickly, you would actually see the broom not moving at all! This is because it has no time to react to your motion before the direction of motion suddenly changes, so it'll just sit there and watch you.

Now let it swing freely again, and then try to oscillate it really really slowly with your hand, and compare the amplitudes when it's swinging naturally, and when you are trying to oscillate it really really slowly. You'll probably notice a slight difference: when you try to interfere with the oscillation, sometimes you are going against the natural movement of the broom, and hence you are slowing it down and decreasing the amplitude.

It all sounds pretty confusing, but when you try it, it's quite apparent.

Now try to move your hand back and forth at the same frequency at which it is naturally swinging. I'm sure you'll see the difference: the amplitude of the swings will increase greatly, because your force is always going with the direction of motion, so you are making the oscillations greater.

So this is the lesson we learn: if we try to oscillate anything at its natural frequency, it will produce an oscillation with very large amplitude, that will increase with time if you continue to make it oscillate. This phenomenon, where you try to make something oscillate at its natural frequency to produce really big oscillations is known as resonance.

So here's how we break glass with our voices: we tap the glass to hear the sound it produces: this sound is the natural frequency of the glass. We then match our voices to that natural frequency (we just have to match the pitch of the note: what we hear as pitch is actually the differences in frequency) and try to oscillate the glass molecules at its natural frequency. Due to the phenomenon of resonance, the glass molecules will develop very high amplitude oscillations. If these waves are large enough to break the bonds between molecules (just like they were strong enough to break the bridge apart in my opening picture) then the glass will shatter!

I don't think it's easy to do, but at least it is possible in theory.

Thursday, April 12, 2007

Radio

In class I mentioned a little bit about radio waves. Here I will mention a little bit more.

If you could see all the radio waves around you, you would literally be blinded: not only are there all the radio signals coming from all the different TV and radio signals, there are also radio waves transmitted by the police, the army, the civil defence, the air force, commercial flights, GPS signals and much much more.

Each of these signals are the form of a typical transverse wave. The information is encoded in two ways: AM or FM. AM stands for amplitude modulation, which basically means the different information is encoded in the varying amplitudes of the wave. FM, frequency modulation, means that the changing frequencies of the wave can be interpreted and translated into real pieces of information.

A radio set typically consists of two things: a transmitter, and a receiver. Their names should tell you what they do: a transmitter takes some information, let's say something that is being said in the form of a sound wave, and turns it into a radio wave (either FM or AM). A receiver does the exact opposite. Both of these things make use of antennae to transmit or receive the info.

A transmitter is pretty easy to imagine: basically you do what would be the equivalent of turning a switch on and off again and again to produce an electric current wave. This electrical wave is then sent to an antenna, which is essentially just a straight wire, where the current moving in this antenna will be converted into radio waves.

Of course the electric current wave will have either its amplitude or its frequency changed over the course of time, which encodes information in the wave. So, when I receive the wave, the radio can produce the sound of music or some kind of information by observing the changes in amplitude or frequencies over time.

When radio waves arrive at an antenna, it will cause an electric current to flow within the antenna. This current will then flow to the receiver. There are thousands of radio waves arriving at the antenna, but the receiver can be adjusted electronically to filter all but one frequency. How? You can read up about the concept: it's known as resonance, which is also the process by which a singer is able to break a crystal glass, although in a very different way.

The current that is filtered through is then passed through a demodulator, a series of complicated electrical components that will break up what is encoded in the wave and then sends the appropriate electrical signals to the speakers. Along the way, the signals are amplified, so that we can hear the signal clearly.

This is of course much too simplistic. For more information, you can check out howstuffworks: http://electronics.howstuffworks.com/radio.htm, which gives a good explanation of radio, and a good explanation of many other things that you can check out for yourself.

Process

Acquiring knowledge is a difficult process. I understand that feeling. Even up till now after studying 4 years of official physics, together with some outside reading, I know virtually nothing, and that is really frustrating sometimes.

While teaching you guys physics, I too am learning physics, but unlike you I have a teacher that I can only turn to through e-mails, and can get to see only when I'm free, and currently, I'm not very free. He told me rather bluntly last meeting that what I was struggling to understand was the very basics of quantum mechanics, and even though I know he didn't mean it as a "you suck" kind of statement, it still hurt rather deeply.

I'm incredibly grateful for someone like him to take the time off to teach a complete beginner like me, but sometimes it really is awful sitting down next to him, watching him write things that you only have the slightest clue of, and not knowing whether to pretend to know, or admit that you know absolutely nothing. I know that feeling all too well.

I know what it feels like to flip through a textbook, or to see things that hardly make any sense. It's a sinking feeling, a feeling of being like a drop in an ocean, of being absolutely stupid and ignorant. Of being defeated, and tired.

And it's absolutely true too. We are too stupid to comprehend physics. We are too ignorant of the things that go on. Most things are too complicated for our small minds.

And guess what, I'm really glad you've realised. If you don't realise that you know absolutely nothing, then that is truly foolish behaviour. No single person is smart enough to be familiar with the entirety of anything.

Many people turn away from anything remotely to do with knowledge once they get to my age. Every single thing is eclipsed by the practical nature of the world: a need to be financially secure or wealthy, a need for social status and prestige, a need for power even. You don't remember what you liked in school, you don't remember what inspired you, you only see what lies ahead. No one has time to ponder the stars. Or music.

But just for one moment I hope you can see how much bigger than the self physics is. Not only physics, but any discipline you can name: mathematics, chemistry, biology, history, geography, literature, music, art etc., each discipline gigantic in itself. They are an attempt to describe something much bigger than yourself. Something that will still be here forever when you die and cease to exist. Something that trillions of people after you will come across again, and hopefully with each person that encounters it, it will become more complete.

So don't turn away because you can't understand. Turn towards it because it is truly greater than you, and the things that you take away from it will help you see the world around you in an entirely new light. Look beyond yourself, and hate the ignorance that you have. Cure it. We all know absolutely nothing, so it is not surprising that everything looks so difficult. But fight the ignorance. Think till you feel like you can't think anymore, question till you get all the answers, look for the answers till you just can't bear to search any more, and when you've finally understood, it's an amazing feeling. You'll feel like you know a dark secret that has been told only to you, and you'll realise how incredible the world around you is.

Tuesday, April 10, 2007

Doe a deer, a female deer.

To all readers, even if you are totally estranged from music, which is difficult to believe, you would have heard of the infamous Sound of Music song from which the title comes. So, even armed with as basic an idea as that (there are 7 basic notes that go into making a simple song, and these 7 notes make up what we call a scale), you can probably understand a good part of what's coming.


You can probably tell the difference between a poor singer and a good one, as they are singing to music being played. You don't really know how you can tell, (musically, you can say that the singer is out of tune, or perhaps if you can tell you would say he is singing "flat"i.e. too low, or singing "sharp" i.e. too high) but you can just tell when someone isn't singing well. There's an almost physiological response to poor singing, or to music that is simply out of tune, and likewise there is a feeling of pleasure when you hear an orchestra that is perfectly in tune with each other, or two singers singing in harmony.


Have you ever wondered why we respond to harmony? How do we know when a singer is singing well? How are people able to tell whether an orchestra is playing well, or if a certain instrument is in tune or not? The answer, and I must admit I never fully realised this until quite recently, lies in physics.


If you ask the nearest choir members, or person with an instrument, to play or sing a low "do" and a high "do" together (remember "that will bring us back to doe!", so after "ti" in the music scale, the next note is called "do" again.) you would hear an amazing thing: the two notes sound like one!


As a physicist, if you were able to dissect the voice box of the said choir members, or just simply observe the instruments in action, you would observe something very interesting about the sound produced: The frequencies of the sound would be in the ratio of 1:2.


A quick example for more music familiar people: A concert A has a frequency of 440 Hz. The A above that, A', would have a frequency of 880 Hz. Likewise for any two notes an octave apart. The higher note will be twice the frequency of the lower one.


Now, it turns out that any two sound waves that are produced that have a very nice ratio, for example 2:3 (you can do this by playing "do" and "so", "re" and "la", or "mi" and "ti" together, known as perfect fifths), or even 4:5 ("do" and "mi", "fa" and "la", "so" and "ti" known as major thirds) sound nice. If you don't believe me, you can go try it on any instrument, or simply sing it. On virtually any music that you can hear on the radio, every time you hear two singers singing, most of the harmonies will be in either perfect fifths or major thirds. (Of course this is outrageous to the musically very literate: what of minor thirds, minor and major sixths, and perfect fourths? Undeniably present. But don't forget, in music we can't simply have harmonies, that would make for very boring music. Music is made interesting by disharmonies that are then subsequently resolved into harmonies. So even notes that don't sound good together are useful!)


Okay.


Now for the more musically literate: This is what I'm actually talking about so far: the harmonic series:



Okay. So what is this diagram? Starting from the really low C on the left, if I double its frequency, I will hear the C one octave above it. If I triple the frequency, it would turn out to be the G third from the left, etc. So each multiple of the original frequency will produce a note that gets increasingly less harmonious with the note before it. Of course, 1 and 2 are extremely harmonious: the octave. 2 and 3 form the perfect fifth, 3 and 4 the perfect fourth, 4 and 5 the major third, 5 and 6 the minor third, 6 and 7 the major second, 11 and 12 the semitone. You can see for yourself that the harmonies get less and less pleasant. Dissonances like the tritone occur at 8 and 11 (terrible ratio, 8:11), and augmented fifth (8:13) etc. etc.

We can construct the harmonic series from any starting note of course. Let's try it from A (concert pitch)

A: 440 Hz

A': 880 Hz

E'': 1320 Hz

A'': 1760 Hz

C#''': 2200 Hz

E''': 2640 Hz

G''': 3080 Hz

Okay. Now let us do something here. If G''' is 3080 Hz, then G'' must be 1540 Hz, G' 770 Hz, and G itself 385 Hz. Let us construct a harmonic series from this G:

G: 385 Hz

G': 770 Hz

D'': 1155 Hz

If D'' is 1155 Hz, then D' must be 577.5 Hz, and D must be 288.75 Hz. Now, let us construct a harmonic series from this D:

D: 288.75 Hz

D': 577.5 Hz

A': 866.25 Hz

This means that the A constructed from this harmonic series is 433.125 Hz, a whole 7 Hz different from the original A at 440 Hz!!

What has happened? Long ago, musicians realised this problem: that starting a harmonic series from one note will form notes that are unique to that harmonic series. If you wish to change keys, say from A Major to D Major, if we insist on using the notes formed in the harmonic series of A to play in D Major, the sound would be horribly off key. Modulation was rendered impossible (not to mention to problems this caused for the french horn and other brass instruments: a separate topic, but well worth exploring!), and without modulation, music got boring fast.

Until a certain Johanne Sebastian Bach came into the picture. He had a wonderful solution to this problem: why not make every single note equally out of tune in such a way that ALL keys will sound equally out of tune? Of course, this sounds disagreeable: if it's out of tune, wouldn't we know it's out of tune and hate the music being played?

Turns out that isn't true. He wrote the Well-Tempered Clavier, a set of 24 preludes and fugues in all 24 keys to show that it was possible to do such a thing. Initially, I would think people were rather uncomfortable with the poor tuning, but today we are so used to his system that what we think is in tune today, would probably have been considered badly out of tune in his time!

Thursday, April 5, 2007

c, The Universal Speed Limit

What is the highest possible speed that can be attained by any object?

Logically, you would think that there would be no limit. As long as there's something to exert a force on the object to accelerate it, it would keep increasing its speed. That sounds pretty much like common sense. If you still remember Newton's 2nd Law, it would make sense too: as long as there is a net force being exerted on the body, it will continue to accelerate.

But sadly for us, logic sometimes takes a back seat when it comes to physics. In 1905, a relatively unknown Swiss patent clerk by the name of Albert Einstein wrote three revolutionary scientific papers and published them all at the same time and all in the same publication, at the ripe old age of 26. One of the papers dealt with an entirely new physical theory which was necessary for reasons that I'm not going to explain, known today as the special theory of relativity.

Of course, I'm not going to go into the details of this subject (which is seriously interesting in its own right: You can check out Twin's Paradox ) but one of the predictions it made is that the greater the speed at which you are travelling, the more difficult it is for you to increase your speed.

So, if you are travelling very near the speed of light, it would take the equivalent of a nuclear explosion to increase your speed by just a few fractional metres per second. This also means it takes an infinite amount of energy to get your speed up to the speed of light, hence making speed of light travel impossible.

Putting that in the context of space travel makes it all sound almost impossible. The nearest star to the Earth is Alpha Centauri (I think? One of the nearest stars at least), and that star is about 4.3 light years away. Even if humans were to travel at the speed of light, it would take them 8.6 years to make the trip there and back.

Over the course of history many people have tried to measure the speed of light, or at least have tried to guess whether the speed of light is finite or infinite. We know now that it is a finite 3 x 10^8 ms-1, but the ancients couldn't have known. So here are some of their thoughts, and ingenious (sometimes not very ingenious, but only on hindsight) methods to determine this speed.

Early philosophers (remember the earlier article: science and philosophy were not distinct disciplines until relatively recently) did not have a unanimous opinion. Some philosophers believed that light, being something in motion, must have a speed, while others believed that it was a stretch of the imagination to believe that something can move with such great speeds, and so believed light to travel instantaneously.

This was all very unscientific of course. The first scientist to think of a way to measure the speed of light was none other than Galileo. He placed himself and another student on two hills 1 mile apart, and, by uncovering lanterns and asking his student to note the time at which he saw the lantern uncovered, and comparing that with the real time at which the lantern was truly uncovered, tried to detect if it took any time at all for the light to travel a distance of 1 mile. Of course, this experiment was a spectacular failure, and he was unable to conclude much.

The first good method was carried out by an astronomer known as Romer, who was observing the orbit of one of Jupiter's moons, Io. Io revolves around Jupiter much like our moon, and when you point your telescope at Jupiter in the sky, you can see Io (if it's a good telescope) go behind the planet and becomes blocked by Jupiter, and then reappear again. Romer noticed that the time taken for Io to disappear and reappear again got longer and longer as Earth moved further and further away from Jupiter, and reasoned that this was due to the greater amount of time needed for light to travel between Jupiter and the Earth as we got further and further away.

A quick and ingenious calculation gave him a very good answer indeed for his time: 2.3 x 10^8 ms-1, which is just about 20% off. Not bad for an astronomer in 1676.

Something interesting to mention here: Imagine a bug walking in front of a projector like the projector in your class. It casts a shadow on the screen, so you can see the shadow of the bug walking across on the screen. Now, if we put the screen very near, the shadow would appear to be moving at roughly the same speed as the bug. But as we move the screen further away, the bug's shadow appears to move faster and faster (for those of you who fall asleep at night watch shadows cast on your ceiling by cars driving by outside, many times you'll see the shadows whooshing by). Do you think that by moving the screen further and further away we can make the bug's shadow travel at speeds greater than the speed of light?

Think about it.

Monday, April 2, 2007

Galileo Galilei

A study of physics is made even more remarkable by studying the history of physics, and this man, Galileo Galilei, is often regarded as the father of modern physics.

In the initial phase of the development of human thought, science was considered indistinguishable from philosophy, which of course in itself is properly founded on logic. So people like Aristotle could say things like this:

All bodies move towards their natural place. For some objects, like cannonballs and human beings, the natural place for them is towards the Earth, and so they fall towards Earth. Other objects, like steam, belong to the celestial spheres, and so they rise up the heavens.

Of course, by modern standards of physics, this way of speaking is totally insane, simply because it is attributing a reason that seems to have no real logic. I could say:

Students in RI got into RI because they were born to be in RI.

Actually, the statement in itself is logical. It explains pretty much everything, but the thing we all take offence with is the fact that the statement isn't based on facts. The logic also works in reverse: if an object rises into the air, its natural place must be in the stars, not the other way round. We can't find an object that we know for sure belongs to the stars, and try to assess whether it rises into the air or not, because the very definition of belonging to the stars relies on the fact that it rises into the air naturally. There's no way to test such a statement.

And this attitude of needing facts to back up any statement that is made, making statements that can be falsified, making positive conclusions that allow us to make predictions (e.g. RI students get into RI because they have a high IQ: a statement that isn't necessarily true, but at least we can test it), all starts with Galileo.

Galileo was the first guy to realise the need for experimentation to back up any findings and any statements he may make. He reduced statements to mere hypotheses, that must be supported by experimental data: measurements taken from experiments.

And how do we associate measurements, numbers that we obtain by observing certain physical quantities such as height, mass, time, length etc. with these statements?

Mathematics, of course.

Galileo is famous for quipping "the language of God is mathematics". Not that he would know, since he was quickly branded a heretic by the Church. But the experiments that he designed, and the measurements that he took to prove the hypotheses that he made are no doubt brilliant.

In Galileo's time, heavy objects were thought to fall at a greater speed compared to lighter ones, as would seem "logical". But once again, logic without evidence was considered useless to Galileo. In a famous series of experiments on top of the Leaning Tower of Pisa, he dropped balls of different masses to seek evidence for the constant acceleration due to gravity. Indeed, from some of his work, he even managed to conclude that: In other words, the distance travelled by an object when dropped from rest is proportional to the time elapsed squared. This approach to science, which is so deeply in-grained in our psyche that today it is taken as a thing that is most natural, was most revolutionary. Today, we call this approach to science (of course, today much more advanced, but fundamentally still the same as the method of Galileo) the scientific method.

When astronauts first landed on the moon, one of the activities that they did was to drop a golden hammer together with a feather on the surface of the moon. Galileo, who could not have foreseen this happening nearly 400 years ago, would probably not have been surprised to see both the golden hammer and the feather hit the ground at the same time. This stands as testimony to the brilliance of mind of the man who many consider to be the first modern physicist.

Disclaimer

First, I must emphasise that this blog is probably not going to be 100% accurate, because the suddenness of the occurrence of this idea gives a good hint as to the unthinking nature of this project. It is a gigantic task I've taken on to write weekly (at least weekly. You must prod me on this) about a subject that is supremely immense and extremely esoteric at the same time, that, sadly I must admit, I have scant knowledge of. But anything and everything to get you interested in some of this stuff.

In all the posts that are to come, I hope to take you through topics that hopefully have some relevance to what we are doing in class, although I can foresee myself getting side-tracked by other equally, if not more interesting things along the way. I will try to avoid any form of mathematics for the benefit of those who have grown to dislike the mere possibility of the existence of such an abominable subject, although, inevitably, physics being a mathematical science and all, I will throw in things that you at least can comprehend at some level.

The goal here is this: for you to read the stuff here and realise that what I'm talking about in class is much greater than the technical dryness that necessarily comes together with being a novice in the subject, for you to realise that without technicalities and fundamentals, you will fail to understand the intricacies of the greatest achievements in human thought on the nature of the universe, and for you to appreciate the fact that what you are doing in class has a meaning, and more than that, a beauty.

Do I seem a little insane? Talking like that? I hope so. And I hope you'll join me in this insanity too.