1、The Physics of Brass Musical Instruments,Or, what do horn players do with their right hands, anyway? Brian HolmesSJSU Dept. Physics, ,Intended structure of this talk,Standing waves Waves in tubes How to build a trumpet What horn players do with thei right hands (anyway).,Actual structure of this tal
2、k,One skit A skit Another digression (if time allows) Much rushing to leave out material I nearly included,79 181 304 428 545 670,Playing frequencies of straight tubeLength: 1.41m,cyl,f,79 181 304 428 545 670,Playing frequencies of straight tubeLength: 1.41m,f,79 60.3 60.8 61.1 60.6 60.9,f/odd,v/4L
3、= 60.4 Hz,cyl,79 181 304 428 545 670,What happens when you add the bell,f,cyl,f,bell,93 221 334 449 574 691,79 181 304 428 545 670,What happens when you add the bell,f,cyl,f,bell,93 221 334 449 571 691,f,14 40 30 21 26 21,79 181 304 428 545 670,What happens when you add the bell,f,cyl,f,bell,93 221
4、334 449 571 691,f,14 40 30 21 26 21,% change,- 22 9.9 4.9 4.8 3.1,The bell raises all the frequencies; but it raises the low frequencies more than low frequencies.,Interpretation: the effective length of the instrument is different from the actual length. High frequencies reflect closer to the open
5、end than low frequencies do. The bell acts as a high-pass filter. Above a cut-off frequency, no sound is reflected back to the lips. The cutoff-frequency is higher for a more rapidly flaring bell.,Why make the bell an ineffective radiator of sound?,Because that makes the bell effective at reflecting
6、 sound back to the lips. The sound returning to the lips gives feedback to them, controlling their vibrations and feeding more energy into the standing wave. This control makes the instrument easier to play.,The mouthpiece has a bowl-shaped cup that connects to the conical backbore.The backbore conn
7、ects to the conical leadpipe of the instrument.,The column of the cup determines a popping frequency. Any sounds near this frequency will be amplified. The popping frequency of the trumpet mouthpiece is near 800 Hz. A deeper cup will result in a lower popping frequency, yielding a less strident tone
8、 quality.,79 181 304 428 545 670,What happens when you add the mouthpiece/leadpipe,f,cyl,f,bell,93 221 334 449 571 691,93 232 348 465 578 696,f,trumpet,Again the frequencies rise; and again, the low frequencies rise more than the high ones.,79 181 304 428 545 670,What happens when you add the mouthp
9、iece/leadpipe,f,cyl,f,bell,93 221 334 449 571 691,93 232 348 465 578 696,f,trumpet,The playing frequencies are a set of multiplesof 116 Hz; except for the first multiple.,f /integer,tr,93 116 116 116 116 116,What if you put holes in the side of a trumpet?,The result, a keyed trumpet, would have unev
10、en tone quality.,Keyed bugles had a more even tone quality, but didnt sound like trumpets.,Other keyed instruments met with even less success. For example, the Serpent.,And the Ophicleide.,To restore resonances above the cutoff frequency. To improve the tone quality of notes below the cutoff frequency. To adjust the intonation of the instrument. To allow for special muting effects.,Why do horn players keep their hands in the bell, anyway?,open,stopped,http:/www.phys.unsw.edu.au/jw/brassacoustics.html,A good on-line reference,
