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

550 18. Music and Musical Instrumentsaction essentially constitutes a servomechanism setup, where the key activates arelay that opens the wind chest to the organ pipes.Because of the large size and number of pipes, organs require large amountsof air for actuating the pipes. The air pressure required is quite small, rangingfrom about 1 kPa gauge pressure for the early hand-powered organs to as much as12 kPa air gauge pressure in some modern units. The air supply for modern organsis provided by an electric fan or an electrically driven centrifugal pump.Lip-Reed InstrumentsIn these types of instruments, the lips serve as the reeds and the air supply isprovided by the lungs. The puckered upper and lower lips can be imagined as apair of double-mechanical reeds of Figure 18.33, with the operational principlebeing virtually the same. The frequency of the pulses, which occur as a resultof the lips throttling the airflow, corresponds to the resonant frequency of thelips combined with the associated instrument. Because the coupling between thelips and the instrument’s mouthpiece is fairly loose, the fundamental resonantfrequency of the lips must correspond to that of the instrument. However, thecombined resonant frequency of the horn and the lips can be varied slightly up ordown by changing the tension of the lips, thus changing the resonant frequencyof the system. The modern lip–reed instruments are the bugle, trumpet, cornet,trombone, French horn, and tuba—collectively referred to as the brasses.The simplest of the brass instruments is the bugle, which consists of a cuppedmouthpiece attached to a coiled tube with a low rate of taper, terminating in abell-shaped mouth. The length of the air column is fixed; there are no valves,and the number of notes that can be played is limited. The overall length of thestandard bugle is about 57 cm, and the notes it can play are C 4 ,G 4 ,C 5 ,E 5 ,G 5 ,B 5 ,and C 6 .As it is equipped with three sets of keys that operate piston valves, the trumpetis a more versatile instrument than the bugle. The trumpet is constructed of acoiled tube almost 3 m in length with a slight taper, terminating in a bell-shapedmouth. The first third of the tube is almost circular, with the remainder slightlyconical except for the last 30 cm that flares into a bell-shaped mouth. Pushingdown on the keys of the piston valves adds to the effective length of the tube.With three valves closed and opening them singly, opening in three different combinationsof pairs, or with all three valves opened, it becomes possible to obtaineight different lengths of the resonating tube. A tuning slide or bit is provided sothat the resonant frequencies can be matched with other instruments. The trumpet,which has an overall length of 57 cm, covers about three octaves, from E 3to B 5 . A mute in the form of a pear-shaped piece of metal or plastic can be insertedinto the bell in order to change the quality of the tone and attenuate theoutput.Only about 36 cm in overall length, the cornet is a smaller version of thetrumpet. In addition to its size, the cornet has a bore that is tapered rather than