The Plucked String - Harman Atwal

PHYS 210 PROJECTS --> here

OK, I've put in a couple of hours in looking at more project ideas, here is what I got, let me know! (These are just topics.)

1) Riccati equation

2) Plotting Jaccobian elliptic sine function

3) Fermat's principle and Mirages

The next two are really interesting!

4) Get a function, define it over a range, and then use maple to derive the fourier series over this range and then graphically compare the exact function with the series as the number of terms is increased. Also, then perhaps discuss the nature of the series in terms of whether the function is even or odd.

This would indeed be a nice teaching/learning aid for Fourier transforms. First Google it to make sure it's not already out there. -- Jess 16:32, 21 September 2008 (PDT)

5) A plucked string question...let the initial shape be given by something and then verify that the motion can be described by a Fourier series solution...I have never done any animating before on maple, but it seems REALLY cool and then just to make it more interesting I could animate the solution for parameter values of my choice? (I know this one does sound a bit hard, but it seems really interesting and I am sure you can help me if I do need help?? Also, I went to the library and picked up a couple of books on maple to help me work through this project.)

It would be hard in practice to actually give a stretched string an arbitrary shape, but it might be interesting to see how various shapes would evolve in time after you "let go". For starters you could just make a real "pluck" shape (a sort of very flat oblique triangle) and see how that goes as a function of where the "peak" of the triangle is (i.e. where the string is plucked). I'm not sure maple is your best choice for animations; maybe MatLab would be better. Jason, what do you think? Another possibility would be to do it in FORTRAN or C and "record" the displacement at the position of a "pickup" as a function of time. Then you could speed up the recording and send a digital voltage to a speaker and actually produce the sound that this virtual string would make on an electric guitar. Be sure to put in some damping, though. -- Jess 16:32, 21 September 2008 (PDT)

This seems like a cool idea (and relevant to my interests, no less). The material of the plectrum, along with attack strength, shape, place along the string, and direction affects the harmonic content of the strings. (Such as, what if you made the "pick" a finger?) The strings themselves factor in, as well. I wonder if that is able to be modeled? Oh, I hope I don't make it sound any more daunting. S48571087 23:14, 30 September 2008 (PDT)