8.03 at ESG - Notes

Pulses on a Struck String

The explanatory text is Pulses on a Struck String. The static figures in that document may be viewed online, at Pulses on a Struck String - extra figures

The animations work better when displayed separately.

Square Wave Impulse. The time interval is from t = 0 to t = 4.
Parabolic Impulse. The time interval is again from t = 0 to t = 4.
Parabolic Impulse - Bounded String. A periodic wave with fundamental period t = 2 is produced.
The MAPLE commands that produced the above animations may be downloaded or copied:
- Struck String - Release 3
  If the older release can be made to run, the program loads more quickly and the graphics have better contrast. Reducing the number of frames will save computation time.
- Struck String - Release 9 ("Shift-left click" or right-click to download)
  The newer release does the computation for Parabolic Impulse explicitly.
- Struck String - ASCII
  These commands should work in any release, and may be cut and pasted into a MAPLE session.

If we're not careful, some aspects of reflected pulses may be counterintuitive.
Here's a page giving an interesting example

Energy in a Stretched String, featuring animations for an explicit standing wave.
An alternate derivation of D'Alembert's solution, but beware; this uses Fourier transforms and delta-functions.

Comments and Suggestions, especially any errors found, are always appreciated.