A digital waveguide section models wave propagation with two delay lines, six attenuators, and two summers per section

The canonical digital waveguide (DW) section has two signals in both directions (forward and backward traveling waves). Each section contains: two delay lines (modeling propagation time in each direction), two summers, and six attenuators — g and -g (modeling energy loss), and r, -r, 1+r, 1-r (modeling reflection and transmission at the junction between sections). The reflection coefficient r determines how much energy bounces back vs. passes through each junction; r=1 creates a rigid termination (total reflection), r=0 means no reflection. Frequency-dependent behavior is modeled by replacing scalar attenuators with filters: typically lowpass for r (high frequencies transmit more readily) and lowpass for g (high frequencies are lost faster). Instruments are modeled by cascading multiple such sections.

Examples

A string = two rigid termination sections (r=-1) connected by uniform sections (r=0) with lowpass loss filters. Woodwind bore = sections with varying r to model changing bore diameter.

Assessment

Explain what physical phenomenon the g attenuator models in a string. Why does a string model need r=-1 at the termination points?