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Lecture 7 - X7 XXXX p 1#7 XX Site map | Contact Us Pipes...

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Site map | Contact Us Pipes and Harmonics Why do closed conical bores have the same set of resonances as open cylindrical bores of the same length, whereas closed cylindrical bores of the same length have only odd harmonics starting one octave lower? The bores of three woodwind instruments are sketched below. The diameters are exaggerated. The flute (top) and clarinet (middle) are nearly cylinders. The oboe (right) is nearly conical (as are the saxophone and bassoon). The clarinet is about the same length as the flute, but plays nearly an octave lower. The oboe is closed like the clarinet, but its range is close to that of the flute. For a background to this discussion, it is worth looking at the difference between closed and open pipes, which is explained in Open vs closed pipes (Flutes vs clarinets) , which compares them using wave diagrams, air motion animations and frequency analysis. To compare cylindrical, conical, closed and open pipes, let's look first at diagrams of the standing waves in the tube.
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Three simple but idealised air columns: open cylinder, closed cylinder and cone. The red line represents sound pressure and the blue line represents the amplitude of the motion of the air. The pressure has a node at an open end, and an antinode at a closed end. The amplitude has a node at a closed end and an antinode at an open end. These three pipes all play the same lowest note: the longest wavelength is twice the length of the open cyclinder (eg flute), twice the length of the cone (eg oboe), but four times the open length of the closed cylinder (eg clarinet). Thus a flutist (diagram at left) or oboist (diagram at right) plays C4 using (almost) the whole length of the instrument, whereas a clarinetist (middle) can play approximately C4 (written D4) using only half the instrument. If you have a flute or oboe and a clarinet, this experiment is easy to do. Play the lowest note on the flute or oboe, and then compare this with the lowest note on half a clarinet (ie removing the lower joint and bell). Important : in all three diagrams, the frequency and wavelength are the same for the figures in each row. When you look at the diagrams for the cone, this may seem surprising, because the shapes look rather different. This distortion of the simple sinusoidal shape is due to the 1/r term, which is discussed below.
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