Next  |  Prev  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Ideal String Physics

\epsfbox{eps/Fphysicalstring.eps}

Wave Equation

$\displaystyle \zbox{ Ky''= \epsilon {\ddot y}}
$

\begin{displaymath}
\begin{array}{rclrcl}
K& \mathrel{\stackrel{\mathrm{\Delta}}{=}}& \hbox{string tension} & \qquad y & \mathrel{\stackrel{\mathrm{\Delta}}{=}}& y(t,x) \nonumber \\
\epsilon & \mathrel{\stackrel{\mathrm{\Delta}}{=}}& \hbox{linear mass density} & {\dot y}& \mathrel{\stackrel{\mathrm{\Delta}}{=}}& \frac{\partial}{\partial t}y(t,x) \nonumber \\
y & \mathrel{\stackrel{\mathrm{\Delta}}{=}}& \hbox{string displacement} & y'& \mathrel{\stackrel{\mathrm{\Delta}}{=}}& \frac{\partial}{\partial x}y(t,x) \nonumber
\end{array}\end{displaymath}

Newton's second law

$\displaystyle \zbox{\hbox{Force} = \hbox{Mass} \times \hbox{Acceleration}}
$

Assumptions



Subsections
Next  |  Prev  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Download StringWaves.pdf
Download StringWaves_2up.pdf
Download StringWaves_4up.pdf

``Digitizing Strings Waves in Vibrating Strings'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]