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Helmholtz Motion

A bowed string exhibits a different kind of periodic motion. For the larger part of the cycle, the bow pulls the string aside. During this ``sticking'' phase, the string and bow move at roughly the same velocity. Eventually the string is pulled too far aside, and so it slips back. During the ``slipping'' phase, the string moves at a far different velocity than the bow. This stick-slip motion is named the Helmholtz string motion in honor of Hermann von Helmholtz. He observed this motion using a special measurement device called the vibration microscope, which he designed.

Figure 4 depicts the Helmholtz motion of a vibrating string. The top two frames show that the traveling waves have a more complicated form than the previous examples. However, their sum behaves quite simply-the string is made up of two line segments, the corner of which traces out the shape of a saucer (shown in red for illustrative purposes in the bottom frame, Figure 4).

Figure 4: Helmholtz motion of a vibrating string with rigid terminations
Image continuous-helmholtz

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Download travelingwaves.pdf

``Traveling Waves In A Vibrating String'', by Edgar J. Berdahl, and Julius O. Smith III,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2007-06-10 under the Creative Commons License (Attribution 2.5), by Edgar J. Berdahl, and Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University