Problems

1. Many woodwinds, such as the clarinet, are better modeled with a closed tube end at the head of the instrument [3]. Use the expression
   

   $$k = \frac{r_1^2 - r_2^2}{r_1^2 + r_2^2}.$$ (4)

   
   
   to calculate the reflectance $k_{closed}$ for a closed tube end.

2. Do pressure waves have a node or an anti-node at a closed end?

3. Redraw the signal flow diagram shown in Figure 3 so that it models a woodwind instrument with a closed end at the head.

4. How does this change affect the fundamental frequency of the instrument?