Optically measured torsional waves on cello string bowed at varying bow force

Transverse and torsional vibrations of a cello G string made of steel, product name "Pirastro Chromcor medium". Find string properties below. String mounted on a monochord and tuned to approximately 98 Hz.

Measurements by a high speed camera at 7000 frames per second, on axis with the bowed string (displacement < 20°).

Transverse: optical marker on the string (transverse), 70 mm away from the bridge, 10 mm away from the bow contact point.

Torsional: optical marker at each end of two needles (top, and bottom, each 4mm long, total weight including marker 0.002 g), 70 mm away from the bridge, 10 mm away from the bow contact point.

Manual bowing by experienced player, bowing at the target contact point 80 mm away from bridge, while each individual stroke represents a certain level of bow pressure. Only regular Helmholtz motion is excited on the string. For each level (high, medium, low) the player adjusted bow velocity reasonably.

* Raw data: movies

Torsion3.avi : medium bow force
Torsion5.avi : low bow force
Torsion6.avi : high bow force

* Data, 1st level of abstraction: extracted traces using subpixel tracking

Tables in *.mqa format hold pixel row and column of extracted optical marker (top,transverse, botteom) for respective bow force (3=medium, 5=low,6=high).

* Data, 2nd level of abstraction: angle of torsional displacement as derived from optical markers and geometry, versus bow force

torsion_angle_vs_3_force_levels (eps, and MATLAB fig).

* String properties

mass per unit length    g/m    6.15

diameter    mm    1.19

nominal tension    N    121

transverse wave speed vtra    m/s    133

transverse wave impedance Z0    kg/s    0.93

torsional fundamental frequency    Hz    543

torsional wave speed vtor    m/s    738