# Why do open-closed cylinders resonate at high input impedance?

According to this paper, open-closed cylinders (clarinets) resonate at maxima of input impedance, while open-open cylinders (flutes) resonate at minima of impedance.

Since acoustic impedance is defined as the ratio of pressure to flow, I would naturally tend to think that resonances have to take place at minima of impedance (maxima of admittance). How is it that resonances in the clarinet take place when this is at maximum?

## 1 Answer

The definition of impedance as "the ratio of pressure to flow" means the oscillating pressure and oscillating of the sound wave.

Don't confuse the oscillating air velocity which makes up the sound vibrations in the instrument with the (approximately) steady flow blown through the instrument by the player. The player's air flow excites the resonance because of the action of the reed in a clarinet or the shape of the mouthpiece of a flute, but it isn't the same as the sound. For example blowing into the end of an open cylindrical tube doesn't produce a musical note, but blowing the same amount of air across the end of the tube (in a similar manner to playing a flute) will produce a note by exciting a resonance in the air within the tube.

The article doesn't say how the impedances are measured, and you can get different curves by choosing different positions.

But assuming they were measured where the energy is being input from the player, that point is effectively the open end of a tube for the flute, but the closed end (because of the reed) for a clarinet.

So for the flute resonance you have low (nominally zero) pressure difference from atmospheric but high air velocity, but for the clarinet you have high pressure and low (nominally zero) velocity.

• Thanks @alephzero. What I understand from your explanation is that it is the generator (reed, lip) what is compelled to vibrate whether at maxima or at minima of impedance. E.g. the reed (because it is blown closed) vibrates only at the frequencies of the maxima of the impedance , and these in turn get excited by the reed vibration, with the flute being the other way around (since it is at atmospheric pressure): the jet can only oscillate at frequencies which are minima of impedance. Is this argument correct? – Pablo Dec 29 '18 at 10:32