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

536 18. Music and Musical Instrumentsiron, which also provides dimensional stability necessary to maintain the stateof tune.Three pedals are provided on the conventional piano. The right or sustainingpedal removes all dampers from the strings so that the strings become damped onlyby the soundboards and end supports. The center or bass sustaining pedal removesthe dampers from all the bass strings. The left pedal, or the soft pedal, reduces thesound output by lessening the length of the stroke of the hammers or by shiftingthe hammers so that fewer strings are struck or by permitting the dampers to act.The dulcimer, considered by some to be the forerunner of the piano, consists ofa large number of strings stretched over a frame mount in an oblong box. Thesestrings pass over bridges that are coupled to a soundboard. The oblong box ismounted on legs, causing the instrument to resemble a square piano without keys.The instrument is played by striking the strings with two hammers, one in eachhand. Dampers controlled by a foot pedal are provided. The range of the dulcimeris from D 2 to E 6 .18.10 Wind InstrumentsA wind musical instrument is a device that generates sound by (a) blowing a jetstream of air across some type of opening, as in whistles, flutes, or piccolos, fifeand flue organ pipe; or (b) by buzzing of lips (acting as reeds) of a bugle, Frenchhorn, trumpet, tuba, or trombone; or (c) by vibrating a reed (or a double reed, i.e., aset of two reeds) through the means of airflow in an accordion, clarinet, saxophone,oboe, bagpipe, English horn, bassoon, sarrusophone, and the human voice.The reed instruments fall into two sub-categories: one category entails instrumentsin which air pressure tends to force the reed valve open (the human larynx,buzzing lips of brass instruments, and harmonium reeds); the other category includesinstruments in which the air pressure forces the reed valve to close (e.g., clarinets,oboes, similar woodwinds, and organ reed pipes). The first category tends toact as a sound generator over a relatively narrow fundamental frequency range, justabove the fundamental frequency of the reed. The other category serves as a soundgenerator over a wider range of frequencies, just below the resonant frequency ofthe reed—but some type of coupling to a pipe resonator must be provided.Figure 18.23 illustrates two possible configurations of a vibrating reed generator.The reed generator is really is a pressure-controlled device for cutting off andreinstating airflow at selected frequencies. In both cases of Figure 18.23, the blowair pressure p b (gauge pressure, relative to the atmospheric pressure) is appliedfrom the left. If p b > 0 (i.e., the blow pressure is above atmospheric pressure), thevalve in (a) is forced closed by the positive pressure and the valve in (b) is forcedopen. The opposite situation occurs when p b < 0. In general terms, the motion ofa reed can be described by (Fletcher and Rossing, 2004).[ d 2 xm r = + 1 ]dxωdt 2 r + ωr 2 Q r dt(x − x U 20) = γ gr (p b − p) + γ be|x| 2