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Equation of the Day #1

Posted by Akano Toa of Electricity , in Math/Physics Oct 11 2012 · 149 views

Waves Physics
So, I've decided to do one of those daily-like blog entries, though I can't guarantee that I'll be able to do this every day (being a busy grad student and all). I figured that, being a physics grad student, math might be one of my stronger suits (next to reviewing LEGO sets), so I'm going to try and share an equation with you and see if I can explain it well enough for people to understand. 8D

Tonight's equation: The wave equation.


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This says that the sum of the change in the change in the function, ψ, with respect to the coordinates used to represent it is equal to the inverse square of the speed of the wave,c, modeled by ψ times the change in the change of ψ with respect to time.

This equation is the governing equation for all wave phenomena in our world. Sound waves, light waves, water waves, earthquakes, etc. are governed by this mathematical equation. In one dimension, the wave equation simplifies to


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which has the lovely solutions

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where A and B are determined by appropriate boundary conditions, and ω/k = c. This equation governs things like vibrations of a string, sound made by an air column in a pipe (like that of an organ, trumpet, or didgeridoo), or even waves created by playing with a slinky. It also governs the resonances of certain optical cavities, such as a laser or Fabry-Perot cavity.

Since waves are one of my favorite physical phenomena, I find it very appropriate to start with this one. ^_^

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Ugh, wave functions are very annoying when you haven't taken diff. equations. :P
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Akano Toa of Electricity
Oct 11 2012 09:08 PM
Yeah, Differential Equations is a very good class to have in your arsenal of physics/math knowledge. :)

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The Duchess Approves
Oct 12 2012 12:32 PM
The answer is 42! And that's my answer for all of them. I solved it with a towel.
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About Me

Akano Toa of Electricity
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Name: Akano
Real Name: Forever Shrouded in Mystery :P
Age: 25
Gender: Male
Likes: Science, Math, LEGO, Bionicle, Ponies, Comics, Yellow, Voice Acting
Notable Facts: One of the few Comic Veterans still around
Has been a LEGO fan since ~1996
Bionicle fan from the beginning
Misses the 90's. A lot.
Twitter: @akanotoe

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