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Elements of a Basic Bowed String Model

\epsfig{file=eps/vinout.eps,width=10cm}

\epsfig{file=eps/modelb.eps,width=10cm}
Structure of a basic model of a bowed string.

This model supposes that the bow is applied to a single point $ p_b$ in the string. When $ v_b=v$ , bow and string stick together, otherwise they are sliding.


$\displaystyle v$ $\displaystyle =$ $\displaystyle v_{o_n} + v_{i_n}$  
  $\displaystyle =$ $\displaystyle v_{o_b} + v_{i_b}$  

The contribution of the reflected waves $ v_{i_n}$ and $ v_{i_b}$ are summed at the contact point:

$\displaystyle v_h=v_{i_n}+v_{i_b}
$

Bow string interaction is represented by the following relations:

\begin{displaymath}
\left\{
\begin{array}{lclr}
f & = & 2\; Z \left( v - v_h \right) & \\
f & = & \gamma \left( v - v_b \right) &
\end{array}\right.
\end{displaymath}

Once this coupling has been solved, the new outgoing waves $ v_{o_n}$ and $ v_{o_b}$ are calculated by the following equations:

\begin{displaymath}
\left\{
\begin{array}{lcl}
v_{o_n} & = & v_{i_b} + \frac{f}{2Z} \\
v_{o_b} & = & v_{i_n} + \frac{f}{2Z}
\end{array}\right.
\end{displaymath}


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Download stiffbowed.pdf
Download stiffbowed_2up.pdf
Download stiffbowed_4up.pdf

``Impact of String Stiffness on Virtual Bowed Strings'', by Stefania Serafin<serafin@ccrma.stanford.edu>, (From CCRMA DSP Seminar Presentation, Music 423).
Copyright © 2014-03-24 by Stefania Serafin<serafin@ccrma.stanford.edu>
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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