3. Clark - Superscope


  4. Superposition patterns



  6. xtra stringy


  7. The interesting question is why does this phenomenon occur when the string simulation doesn’t explicitly use the fourier series?

    All that happens is each point has a displacement and velocity, and these are updated based on the distance between its adjacent points, in order to restore it back towards the center. So basically:

    If i is every ith point on the string of length, then (i+1) and (i-1) act on i with some force. As every i has a horizontal displacement d and velocity v, the force on i is equal to:

    - k( (di - di+1) + (di - di-1) )

    where k is a hookes law spring constant. This rearranges nicely to get rid of the brackets:

    k( di+1 + di-1 - 2*di)

    This just means that each point is accelerated towards its adjacents, but expressed in awkward notation. I’ll draw a diagram at some point.

    But yes, what motivates this really basic simulation to behave like a fourier series, and what aspect of it dictates the maximum number of apparent harmonics?


  8. paraffing asked: Hello! Regarding your latest post, you probably know about fourier series? If there aren't many terms in a series, a square wave function can have those small waves along "flat" regions - they flatten out as you add terms, but I think there tends to be a little bit of an overshoot for a while (Gibbs phenomenon). Sorry if I'm just telling you what you already know!

    Hi! Thanks a lot for the message, I hope you don’t mind that I’ve shared it, mainly because you’ve expressed what’s going on far better than I can.

    I had seen the effect before while playing around with synthesizers (square waves + low pass filters), but I had no idea that it was called Gibbs phenomenon, that is cool.

    There are so many cool science students/graduates out on tumblr that I am kind of secretly hoping that everyone will get involved on here and fill in the gaps in my education.


  9. You know how a square wave is made of the sum of loads of odd numbered cosine harmonics but it can never be perfectly square cos there would have to be infinitely many harmonics? Well, the unusual sharp/curvy edges of the wavefronts here kind of relate to that. Either caused by the resolution of the floating point numbers in python, or the number of points, or the spring constant?


  10. I think the strange jagged edges have something to do with the initial conditions being so sharp (having a high “impulse”), and also the fact that there is no damping/energy loss. Or that it’s just a simulation and i’ve found a case where it behaves incredibly strangely.