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Friday, March 27, 2009
Ok, so I've decided to put down my guitar today. I will not play guitar for more than an hour a day on weekdays, at least until my exam is over.
However, just as I was putting it down, I thought to myself, how can I apply what I've learnt in 113 to whatever I'm doing and I was just thinking about guitar harmonics. I thus decided to derive a mathematical expression for which frets on which one is able to find harmonics.
In music, the most common tuning is the equally tempered scale. Say we have a tuning fork, which gives us the note of concert A at 440Hz. At one octave up, the frequency of the note would thus be twice that of 440Hz, which is 880Hz. The same applies for all notes, an octave up would mean that the frequency of the note would have doubled. The frequency of each semitone from our key note (meaning A# if our key note is concert A) must therefore be some multiple, r, of our original frequency.
So for A#/Bb, we have
f' = r*f,
for B, we have
f'' = r*r*f
and so on. This goes on until we have our octave which is 2 f = f * r^12. Hence, we find that the ratio between each semitone,
(stupid blogger scales the pics weirdly....)
For a guitar string, every time we pluck an open string, we receive a fundamental frequency that is related to the length of the string by f = v /2L. If say we press down within the first fret, this fundamental frequency increases by 1 semitone, as such we have,
which is the length of the distorted string. As such, the ratio between frets is also 1/r, where r is the twelfth root of 2.
Harmonics are produced by creating standing waves on the string (refer to diagram below).
(photo from wiki)
For the open string, or the fundamental frequency, we create a standing wave as in the first diagram. However, to create a standing wave as in the second diagram, we need to create a node (or a non-vibrating point of string) where it is at half the length of the string (this corresponds to the twelfth fret). For subsequent harmonics, we have to create nodes at the fret which corresponds to the corresponding fraction of string.
Furthermore, we know that the sum of all the “frets” (including those off the guitar neck) is the length of the string. As such, we have the following expression. Note that k represents the fret number.
as the series is geometric with a common ratio of 1/r.
For the first overtone, the frequency of the standing wave produced is twice that of the fundamental and as such, is one octave higher than the fundamental.
The length of string required for the first node is half the entire length of string. Thus,
Solving for k, we find that k = 12.
For the next overtone the frequency of the standing wave is 1.5 times that of the fundamental, which makes it somewhere around a perfect 5th.
The length of string required for the first node is one quarter the length of string, thus using the same process, we find that,
and k = 7.
Thus, for any overtone in general, the fret number can thus be found by the eqn,
where n is the n-th harmonic :)
Sunday, March 22, 2009
I was just reading a particular coursemate's blog and it just got me thinking.
Basically, I believe this person made a post (which I didn't manage to read because it was taken down) claiming that physics is the superior science and that only bright people get into physics or something along those lines and drew quite a bit of flak for it....
Though I didn't read the original post, I guess I can understand his frustration. Plus, I pretty much share the view that Physics generally attracts smarter people. Well, perhaps the other subject that draws attracts smart people is Mathematics.
Plus, I believe and know that PHYSICS IS THE MOTHER OF ALL (natural) SCIENCES.
(picture from XKCD)
I believe it's like the people who decide to study law or medicine. People who do decide to go into those fields are usually of a certain "kuan" (hokkien for attitude). I guess it's the same for physics. The kind of people we get are usually of a certain "kuan". Basically, I feel that we're people who want to know more about the world around us. We're people who can't stop asking "Why?" (A la Tay Ping Hui!)and seek to achieve a deeper level of understanding, which requires a certain amount of intelligence to comprehend. This is perhaps why a good number of physics people tend to be damn arrogant and/or irreverant.
Still, this doesn't mean that the physicist is any more important in society and in history than any other profession. Even engineers (who I believe are the oompa loompas of not just science but the economy) have had a key role to play throughout history (the industrial rev, post-WWII modernization, Oliver Heaviside, etc).
But acknowledging this fact doesn't mean that I don't feel frustrated about the way physics is perceived by others (esp in Singapore). I'm pretty sick of seeing people cringe whenever I tell them that I'm a physics major. I vividly remember the face this particular secondary school classmate of mine gave me when I told her that I was going to be a physics major. To this day I feel like punching her. There seems to be this stereotype running amongst people that physics is dry and scary... If I tell people I'm a literature major, I guess people are likely to smile and say, even though it's not practical, you're doing something you're interested in. If I tell people I'm a physics major, they'll first say," Physics!?!? EURGH! Why!?" and this would be followed by," So, you intend to be a teacher is it?".
And this brings me to the next stereotype that certain "arts" majors have about science majors.That science people can't stand literature and poetry and whatnot.... Sure, not all science people have a feeling for the arts. Not all science people can appreciate a poem, catch subtleties in a play and critique a writer's prose. But there are some who can. However, I find that it is the arts majors who are even more intolerant of math and science than science majors are intolerant of arts. The study of Literature is at the end of the day, what I believe is essentially, the "science" of written art. People who are good at both science and art, would choose one. While the science major can still keep track of the arts, the one who chooses the arts quicly falls behind in the sciences.
My point is, it's sad. Sad that, even though physics is so essential to our daily lives, it still remains the most under appreciated of the three sciences. Maybe it's just the Singaporean Businessman mentality which draws more people to the more applied sciences like chem and biology. Perhaps physics just seemed like a scary subject in secondary school and JC (a mindset that I intend to change, at least amongst my students).
From Wiki
Physics (Greek: physis – φύσις meaning "nature") is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its motion. More broadly, it is the general analysis of nature, conducted in order to understand how the world and universe behave.
Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics had been considered synonymous with philosophy, chemistry, and certain branches of mathematics and biology, but during the Scientific Revolution in the 16th century, it emerged to become a unique modern science in its own right. However, in some subject areas such as in mathematical physics and quantum chemistry, the boundaries of physics remain difficult to distinguish.
Physics is both significant and influential, in part because advances in its understanding have often translated into new technologies, but also because new ideas in physics often resonate with the other sciences, mathematics and philosophy. For example, advances in the understanding ofelectromagnetism led directly to the development of new products which have dramatically transformed modern-day society (e.g., television, computers, and domestic appliances); advances in thermodynamics led to the development of motorized transport; and advances in mechanics inspired the development of calculus
Physics is about nature. Physics is about discovery. Physics is about philosophy. And it does not deserve to be treated the way it is currently.
____________________________________________________________________________________Sunday, March 15, 2009
Translation (which should be mostly right) :-
I play the engineer Wang Zhi Wei in the show the Dream Catchers. In whatever he does, (Wang Zhi Wei) will consider the situation around him and then carefully calculate, compare and weigh the options available to him.
Someone has said before, (in English) "Scientists ask, 'Why?', Engineers ask, 'Why Not'?", which means .... (translates the quote into chinese).
If you often say,"Why not?", then you've got an Engineer's DNA. Why not consider studying Engineering, and give the engineering experience a try ;)
Wah lao... I feel insulted as a Physics major lor...
First of all, the quote is total bullshit. It's supposed to be a raped version of a quote from George Bernard Shaw's play, Back to Methuselah. (Thanks to rctay's Windows Live space blog entry which exposed the literary piracy for what it was). The real quote is as such,
If I can do that, what can I not do? I tell you I am very subtle. When you and Adam talk, I hear you say 'Why?' Always 'Why?' You see things; and you say 'Why?' But I dream things that never were; and I say 'Why not?' I made the word dead to describe my old skin that I cast when I am renewed. I call that renewal being born.
Secondly, this is absolutely shameless propaganda. If the government wants more Engineers, they advertise in other ways. If I were an engineer and I saw this, I'd be pretty embarassed myself.
Thirdly, engineers DO ask, "Why not?". They ask, "Why not I disregard gravity when calculating how much force you need to push a block up an inclined plane?". Yeah, for all that engineering is supposed to be Applied Applied Physics, the average engineering major isn't really that great. (Pee is an exception. But then again, he's a CN Yang scholar and taking our physics modules. To Pee: Dude, your physics is Godlike.)
Maybe I'm being a little unfair when it came to the last point, but the first two were enough for me to want to kick Tay Ping Hui in the nuts lor... If I were Tay Ping Hui, I'd be kicking myself in the nuts.....
Anyway, go check out Mosaic happening at the Esplanade till 22nd June. Some of the acts at the Concourse are pretty good but most importantly, it's FREE.
____________________________________________________________________________________Tuesday, March 10, 2009
Ladies, please forgive me as I am about to lapse into pure male-ism for the next few paragraphs.
Megan Fox bending over an opened car hood in Transformers, Elishah Cuthbert by the window in The Girl Next Door, Jessica Alba in her promotional shots for Into the Blue. Sexy, yes. But these are nothing compared to the tag team of guitarist Kaori Muraji and violinist Ikuko Kawai.
The violin weeps in sorrow whilst the guitar morunfully sings a dirge. Both are played by the most beautiful women ever to lay hands on their respective instruments. And with such virtuosity, most people can only dream of being able to play like them.
Such beauty, such grace and such wonderful music..... this shall be in my mind for the longest time....
God, I thank you for Mr Jaoquin Rodrigo, for without which, the Concierto De Aranjuez would never have been composed and without which, the event in the video above might never have occurred.
Apart from Kaori Muraji and Ikuko Kawai, I was treated to the most brilliant private piano recital today, by none other than the virtuoso Jason.
Go Jason.... You R4WK (maybe not as much on piano as you do on guitar, but you still R4WK).....
____________________________________________________________________________________Friday, March 6, 2009
Finally, hall production is over. Thank God our performance itself was good. It sure made me tulan by taking up much of my time but I made friends and I did have some fun while at it. I'm still pretty relieved it's over. No more rushing to go back on Sunday evenings, no more late nights just trying to finish my tutorial. And finally, I'll have time to practice guitar again.
Anyway, the NTU open house is next Saturday, and ironically, the theme for the event is called "Life @ NTU". Wow. How appropriate. Especially since some EEE student stabbed a prof and killed himself after. Oh, and not forgetting the guy who was found dead in his apartment in Nanyang Heights... People sure are Living Life @ NTU. (Thanks Chris for pointing it out to me... no disrespect intended to those who have passed on, but yeah.... this was too much not to say anything about)
I suppose SPMS will also be showcasing something during Life @ NTU, and I would like to warn prospective students of several very misleading advertisements. First, on the NTU SPMS website, there is a little flash animation which shows the faces of several students with a small caption below saying,
LXXng HX FXi,
Physics Major,
XaXXXnal Junior College,
A-lvl 4 As
Now, even though it's good to showcase your top students, that's just going to lower the morale of many prospective students who are not sure if they can make the grade.
They should have put my face on the flash animation,
Teo Wei Ren,
Physics Major
Super-Raffles (aka Serangoon) Junior College
Nearly Failed Sec 2 Mathematics
Took Combined Physics in Upper Sec
C for A-lvl physics
Now that's going to keep applications up. We're not saying that the school is lousy. Oh contrare. We're going to give many prospective students hope :) And from there, the profs can take their pick from the increased number of applications.
This brings us to our next misleading advertisement. This was taken from a standing poster on the level 1 main entrance of SPMS. Can you spot what is wrong with the picture?
Ans:
THEY'RE BLOODY SMILING IN LAB!!!!
For those who have been through PAP118 and 119, you guys know, lab is never an occassion to smile about. You have no idea what the lab manual is saying, you're trying (in vain) to anticipate the viva question (for which you're going to have to bullshit your way through anyway), your lab partner is late, and your readings show no relation to the theory whatsoever... God knows what else....
The only time you DO smile in lab is when you've finished early, and you THINK you're right. They should put up another poster next to this one showing the students swearing in front of their computers while doing their lab report. And maybe a third showing their pissed off faces while redoing the experiment.
Anyway, here's a little clip which I found quite funny... If it's the same guy who came up with Benny lava and he's asian, we now know he's not thaaat racist....
