A bowed string moves in two straight segments joined at a moving corner

Evidence

One complete cycle of the motion of the string immediately under a bow moving in one direction is illustrated in the graph on the right-hand side of Figure 4.8. (When the bow moves in the other direction, the pattern is reversed.) The string moves at a constant velocity when it is gripped by the bow hairs and then returns rapidly through its rest position until it is gripped by the bow hairs again. If the minute detail of the motion of the bowed string is observed closely, for example by means of stroboscopic illumination, it is seen to consist of two straight-line segments joining at a point that moves at a constant velocity around the dotted track as shown in the snapshot sequence in Figure 4.8. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1106

Categorization

Category: Causal Relationships

• SEED: The two-straight-segment, moving-corner model of bowed string motion is a great physics puzzle for an essay on how simple rules produce complex instrument sounds.
• XREF: Connects to the reader’s interest in how mechanical vibration translates to perceived pitched tone in psychoacoustics.

Related

• A bowed string alternates constant-velocity grip with rapid snapback motion (similarity 0.89)
• A bowed string drives the bridge with a sawtooth waveform (similarity 0.86)
• Bowed strings alternate between stick and slip motion (similarity 0.86)
• A bowed string vibrates as a traveling kink, not as smooth standing waves (similarity 0.86)
• Bowed string motion is a stick-slip effect producing a sawtooth wave (similarity 0.85)
• Plucked strings vibrate as a sum of harmonic partials, not as a pure tone (similarity 0.83)
• Bowing forces stiff-string partials into perfect harmonic alignment through phase-locked entrainment (similarity 0.81)
• Bowed strings sustain high harmonics indefinitely while plucked strings lose them quickly (similarity 0.81)
• Increasing string tension raises the frequency of a single-bead oscillator (similarity 0.81)
• The stick-slip bow interaction self-limits and adapts energy to the drain. (similarity 0.80)
• Horsehair’s directional grip enables sustained bowed-string notes (similarity 0.80)
• String vibration is driven by changing force direction, not changing tension (similarity 0.80)
• Bow stick-slip generates a sawtooth Helmholtz wave with rich harmonics (similarity 0.80)
• Coupled string and board modes produce wavering sound rather than steady tone (similarity 0.80)
• A violin string clamped between steel walls would radiate almost no sound (similarity 0.80)