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

546 18. Music and Musical InstrumentsFigure 18.32. The action of a double reed. Air particle velocities are indicated by arrows.the opening between the reeds. The high velocity of the air reduces the pressurebetween the reeds, in accordance with the effect of Bernoulli’s principle.This causes the two reeds to be forced closer to each other, thereby constrictingthe airflow. With the airflow now reduced by the constriction, the pressureincreases, causing the reeds to spring back toward their original position, but owingto their momentum, they moved beyond their original positions. The openingis now at its largest, and the airflow is increased accordingly. The internal pressureon these reeds are now quite small, so they return to their original position,and the cycle begins again with this sequence of events repeating at the rate ofthe resonant frequency. Thus, a steady air stream undergoes a throttling actionthat generates a saw-toothed signal that contains the fundamental and all of itsharmonics.The oboe consists of a double-mechanical reed such as that shown in Figure18.32, coupled to a conical tube with a slight flared mouth. The effective length ofthe resonating air column is controlled by the number of holes that are opened orclosed by the fingers either directly or through keys. The oboe covers three octavesfrom B to G 6 ; the overall length of this instrument is 62 cm. The English hornresembles the oboe in most respects, especially in the key and fingering system,with the principal difference being that the double-mechanical reed is coupled toa tapered conical tube that terminates in a hollow spherical bulb with a relativelysmall mouth opening, thus producing a unique timbre. The fundamental frequencyrange of this 90-cm long instrument covers less than three octaves, from E 3 to B 5 .Approximately 70 cm long, the oboe d’amore is a smaller twin of the English horn,and it ranges over nearly three octaves from G# 3 to C# 6 .The bassoon is a noble-sounding instrument that consists of a double-mechanicalreed coupled to a conical tube that is doubled back on itself so that a lower frequencyrange is provided without compromising the portability of the instrument itself.There is no appreciable flare at the mouth. A set of holes on the side can be opened