Reflection at a Fixed End of String

Consider the displacement of a string at the boundary :

$\displaystyle y$	$\displaystyle =$	$\displaystyle y_r(t-0/c)+y_l(t+0/c)$
	$\displaystyle =$	$\displaystyle y_r(t) + y_l(t).$

If fixed, it's displacement is zero:

$\displaystyle y_r(t) + y_l(t)$	$\displaystyle =$	0
$\displaystyle y_r(t)$	$\displaystyle =$	$\displaystyle -y_l(t).$

$\fbox{ \parbox{5in}{the reflected wave is equal but opposite to the right traveling wave.}}$

Reflection from a fixed boundary:

**Figure:** Damped Vibration, animation courtesy of Dr. Dan Russell, Penn State University.

``Music 206: Digital Waveguides'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).