TABLE OF CONTENTS Let us now forget about percussions and go back to wind instruments, as we examine their resonator: the column of air contained in the tube. Unlike other instruments we have studied so far, the sound is sustained, either directly by the musician blowing into the mouthpiece (woodwind, brass), or by a mechanical blower (organ). We are going to study the case of a cylindrical tube with length L (see Figure 2.9), assuming as a hypothesis that a plane wave is traveling through the tube [5] along the tube's axis Ox. Hence the acoustic pressure p a inside the tube depends only on x and t, and it is simply denoted by p( x, t). The (average) speed of the air particles inside the tube is still denoted by v( x, t). In the simplified model we are describing, the acoustic excitation produced by the mouthpiece is set, and we study the tube's reaction to this excitation. We can then divide the excitations or 'controls' of the acoustic phenomenon into two categories.
Pressure control: in this case, the source of the air vibrations consists of a pressure p E( t) imposed at the tube's entrance (on the left): p(0, t) = p E( t) for any t. This model is an approximation of a flute or of a 'flue pipe' on an organ (which works the same...
