Every object, substance, has a natural frequency at which it is "willing" to vibrate. When an external agent applies a forced vibration that matches this natural frequency, the object begins to vibrate with ever increasing amplitude, or resonate.

 

 

Open-Open Pipes

 

Pipes can either be open on both ends or on only one end. The open ends act as free-end reflectors (producing antinodes) and the closed ends act as fixed-end reflectors (producing nodes). Let's start our investigation with a pipe open at both ends, for example, a flute.

 

Notice in the animation that both ends always remained open or "free" to move, that is they are antinodes. A summary of the first three harmonics for an open-open pipe are shown below.

 

Open-Closed Pipes

 

Now let's examine a thumb piano, an instrument which is open at one end and closed at the other.

 

Notice in the animation that while the open end always remained "free" to move, the clamped end always remains "fixed." The free-end is an antinode while the fixed-end is a node. A summary of the first three harmonics for an open-closed vibrating system are shown below.

 

Observe that there are no "even harmonics" among the resonance states of this type of vibrating system. This stems from the fact that the fundamental frequency is a half-loop or ¼λ. Since every overtone represents the addition of a complete loop, which contains two half-loops, we can never add just one more half-loop. Thus, we cannot generate even harmonics.