Abstract
Steady self-excited vibrations of a bowed string, which is perfectly flexible and subject to negative damping due to solid frictional force of general characteristic and to positive damping due to air resistance only, are studied by means of a Fourier series method utilizing series transformation. It is shown that in the limiting case of air resistance tending to zero the obtained solution reproduces the celebrated Helmholtz mode of vibration for a bowed string. The solution also substantiates Raman's results about the necessary bow force to maintain vibration.
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