Re: How does a flute work?

Hello,

Okay, I'm going to tackle your questions a little out of order. First, let's see why a bottle "whistles" when you blow over it. Here is what the Acoustics FAQ has to say about it:

Why does blowing over bottle make a note ?

Resonance in acoustics occurs when some mass-spring combination is supplied with energy. Many musical instruments rely on air resonance to improve their sonority. If you blow across the mouth of a bottle you can often get a note. The bottle behaves as Helmholtz resonator. The main volume of air inside the bottle is analogous to a spring, whilst the "plug" of air in the neck acts as an attached mass. The resonant frequency is roughly given by

    f =  { c sqrt (S/LV) } / 2pi

    c is velocity of sound 
    S is the surface area of the neck opening 
    V is bottle volume 
    L is the effective length of the neck ie the actual length plus ends
    correction. Ends correction ~ 1.5 times radius of neck opening.

So, when you whistle over a bottle, you set up a standing wave in a vibrating column of air. Basically, this is similar to how a clarinet works. The air blown over the narrow opening of the clarinet is moving fast so, according to Bernoulli's equations, sets up a region of low pressure. This local region of low pressure forces the elastic reed inside the clarinet up, which closes the flow, and then the elastic reed clamps back down to it's closed position. This opening and closing of the reed sets up vibrations in the open tube and acts as a pressure antinode (since the the variation in pressure is at a maximum at the end that you blow on).

A little side note on pressure nodes/anti-nodes and open and closed tubes. If you introduce vibrations in a tube at one end (by putting a speaker at that end, for example), that longitudinal compression wave travels to the other end. If the tube is closed at the other end (closed tube), the wave can vary with it's maximum amplitude and the wave is reflected back from the closed end with no change of phase (see D. Giancoli's Physics, Ch. 17). This corresponds to a pressure antinode (comprable to a transverse wave's antinode which is the area of maximum amplitude of a standing wave). But if the tube was open to the atmosphere at the other end (open tube), the compression travels out into the air and since we can't change the air pressure, this acts as a pressure node (comprable to an area of zero displacement at all times in a standing wave). Thus, the wave is reflected from the node with a phase displacement of 180 degrees (the compression is reflected as a rarefaction).

So the clarinet acts as a closed tube with a pressure node at the open end and a pressure antinode at the reed end. But the flute is actually an open tube with pressure nodes (and displacement antinodes, since displacement and pressure are 90 degrees out of phase with each other) at both ends. It acts much like an organ pipe where blowing air across one edge of the open tube sets up the turbulence in the air that in turn sets up the vibrations in the column of air. The air column resonates at it's natural frequencies of vibration. This is where the fundamental frequency and overtones come into play. These frequencies depend on the length of the column of air (for the specifics, please refer to Halliday and Resnick's Physics, the chapter on sound waves (sorry, I don't have the book with me right now so I can't tell you the exact chapter; but H&R does an excellent job of deriving the equations)). As far as the finger hole placements, those basically serve to change the length of the tube (the column of air) and thus allow you to get different notes (the longer the vibrating air column, the lower the pitch). I'm not familiar with the pan flute, but I believe it's held straight on whereas the "classical" flute is held sideways. Both work by blowing air through or over a narrow opening (the "hole before the finger holes"), thus setting up the turbulence effects discussed earlier, which in turn set up the vibrations in the air column. The open "hole before the finger holes" is also what allows the flute to be an open tube as opposed to the closed tube of the clarinet (this changes the quality of the sound).

The physics of music and instruments (like the flute) can get very complicated and there's a great body of specialized books on this field. This attempt at an explanation barely scratches the surface and at best covers only the gross basics of the subject; if you'd like more detail, I'd recommend going to the local university library and looking up some books on the physics of music. In addition, here are some links that I found on the Web; some of these are very cool, some very basic, and some very advanced... give them a look:

• Flute Acoustics
• Folk Flutes and Pennywhistles
• Sound Reproduction Technology
• FOLKERS & POWELL: Flute articles
• WWW Virtual Library on Acoustics and Vibrations

Best regards,

Rick.