THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

538 18. Music and Musical InstrumentsFigure 18.24. The mechanism of the flue pipe organ, an air-reed instrument. The magnitudeof the pressures are indicated by the diameter of the circles. A dark circle denotesa pressure above atmospheric, and a white circle indicates a pressure below atmospheric.The direction of the arrows represents the direction of airflow, and the magnitude of particlevelocities are indicated by the length of arrows.then enter the pipe, as indicated in Figure 18.24 at θ = 90 ◦ . The excess pressurewill now direct the incoming air stream to the outside at θ = 180 ◦ . This resultsin the excess pressure being relieved and a rarefaction owing to the inertia of theoutgoing air, as shown for θ = 270 ◦ .The decreased pressure pulls in the air to renew the cycle at 0 ◦ . This cycle consistingof the four phases repeats itself at the resonant frequency of the system.The frequency of the complete cycle occurs at the resonant frequency of the closedpipe. Odd harmonics are also produced, because the closed pipe resonates at thesefrequencies as well as the fundamental; this action steers the air stream vacillatingfrom the interior and the exterior. In the case of the open pipe, both odd and evenharmonics are produced. Sectional views of the open-flue pipe (made of metal) anda stopped-flue pipe are shown in Figure 18.25. A whistle, such as that used by policeofficers and referees of athletic contests, operates on the same principal as the organflue pipe except that the resonating chamber is a Helmholtz resonator, which isessentially a chamber with a narrow neck. The resonance of a whistle can be foundfrom application of Equation (7.66), on the basis of the volume of the whistle chamberand the area of the sound-radiating hole coupling the chamber to the outside air.The overtones due to resonances within the small chamber occur at relatively highfrequencies and are effectively suppressed by the inertance of the sound-radiatinghole, thus resulting in a nearly pure tone of the whistle. A calliope is a groupof whistles with frequencies corresponding to the notes of a musical scale. Eachwhistle is controlled by a valve connected to a key that is part of a keyboard similarto that of a piano. Either steam or compressed air is used to actuate the whistles.