The uncorrected equations for the resonant frequency of the nth harmonic for open and closed pipes are for an open pipe, and for a closed pipe. In practice L is the actual length of the pipe only if the diameter of the pipe is very small compared with its length. As this is usually not the case, we have to apply an end correction to the actual length of the pipe to obtain its effective length. However, except for some organ pipes the bore of most wind instruments is not cylindrical and the open ends are flanged. Of these, only the conical and cylindrical pipes have resonant frequencies that are multiples of the fundamental.
L has exactly the same resonant frequencies as an open cylindrical pipe of the same length has.
We shall see later that many wind instruments are part cylindrical, part conical, and part flanged. Thus in playing, in tuning, and in construction the only variable is the length. All wind instruments consist of a sound generator and a resonant air column, or cavity. Air-reed instruments such as the flue organ pipe, flute, piccolo, recorder, flageolet, and fife. Single mechanical reed instruments such as the reed organ pipe, clarinet, saxophone, and bagpipes.