Does the width of a tube effect the sound produced?

Answer 1

The width of a cylindrical tube helps to support the production of pitches and allows for more power in the sound, but it has no affect on the pitch of the tube at all. There is an exception to this rule, but for most purposes, it can be presumed that two cylindrical tubes (pipes) of the same length and different diameters will sound the same pitch.

The canonical definition of the pitch of a tube is based on organ pipes. A cylindrical organ pipe can be open (unstopped at both ends) or stopped at one end. (Stopped infers that the vibrations in the tube do not cause vibration at the stop point, which can be achieved by a wall at that end of the tube. Generally, a Flute-type of pipe is considered open at both ends or closed at the 'far' end, since the 'near' end is where the wind enters and excites the vibrations in the tube. A reed pipe is considered closed at the entry of the tube, and must be open at the other end, or sound won't come out of it at all!)

For an open pipe, vibrations occur at the entry to the tube (where the incoming air excites the vibrations) and the other end (where the vibration couples to the air, and can be heard.) Physics requires that the center of the vibrating air column be a node, where there is no vibration, and the open pipe is said to "vibrate its length". A flue pipe which is closed at the far end has an enforced node at that end, and the entire length of the tube vibrates, so it "sounds twice its length".

The flute is an example of an open pipe, the Clarinet (which sounds an octave lower for the same length) is a closed cylinder. There is another effect in closed cylindrical pipes: they overblow on odd harmonics, and have no even harmonics, or very little of them, in their tone. (Which is another whole question to be answered elsewhere.)

So for a cylindrical pipe, i.e., 'tube', the width of the pipe has no effect on the pitch of the tube. It does have an effect on the strength of the vibration, and may have to be a certain width for that pitch to be formed at all. But the width doesn't change the pitch.

For a conical pipe, where the width of the bore increases from one end, the effect is that the pipe sounds its length whether it is open or closed: this is why an Oboe and a flute sound the same pitches for the same length of tubing, even though the oboe is conical and the flute is (mostly) cylindrical.

Now, here is the one exception to the width having no effect on pitch of a tube: if you have a tube which is 'mildly conical' for most of its length, and then, at the output end, has a 'sudden flare', a great increase in widening over a short space, the actual pitch of the tube is lowered slightly. This effect is seen (when carefully observed) in the Bassoon and some brass instruments.