Shape of a Plucked Elastic Cord
A double-image photograph of a plucked elastic cord is shown below. The flash unit was discharged manually while the cord was being held stationary. Before the camera shutter was allowed to close, the cord was released, thus exposing a second image of the cord. Note the placement of the tape recorder directly below the pluck point. The cord makes very little noise when released, but this trigger is sensitive enough to detect the twang.
It would seem that the cord doesn't travel much slower than sound. In actuality, though, the cord travels much slower. A delay in the response of the trigger accounts for the fact that the cord travels more than half the distance to the microphone before the flash discharges.
If you're interested in why the cord assumes this interesting trapezoidal shape, the theory is presented in many physics texts on waves. Here are two references:
- Philip M. Morse, Vibration and Sound, (American Institute of Physics, 1976), pp.71-89.
- Judith C. Brown, "Time-dependent behavior of strings using Fourier analysis," American Journal of Physics 54, 125 (1986).