1. The Physics of Brass Musical Instruments Or, what do horn players do with their right hands, anyway? Brian Holmes SJSU Dept. Physics, horncabbage@aol.com

2. Intended structure of this talk Standing waves Waves in tubes How to build a trumpet What horn players do with thei right hands (anyway).

3. Actual structure of this talk One skit A skit Another digression (if time allows) Much rushing to leave out material I nearly included

4. 79 181 304 428 545 670 Playing frequencies of straight tube Length: 1.41m cyl f

5. 79 181 304 428 545 670 Playing frequencies of straight tube Length: 1.41m f 79 60.3 60.8 61.1 60.6 60.9 f/odd v/4L = 60.4 Hz cyl

6. 79 181 304 428 545 670 What happens when you add the bell f cyl f bell 93 221 334 449 574 691

7. 79 181 304 428 545 670 What happens when you add the bell f cyl f bell 93 221 334 449 571 691 ff 14 40 30 21 26 21

8. 79 181 304 428 545 670 What happens when you add the bell f cyl f bell 93 221 334 449 571 691 f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.

9. Interpretation: the effective length of the instrument is different from the actual length. High frequencies reflect closer to the open 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.

10. Why make the bell an ineffective radiator of sound? Because that makes the bell effective at reflecting 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.

11. The mouthpiece has a bowl-shaped cup that connects to the conical backbore. The backbore connects to the conical leadpipe of the instrument.

12. 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 quality.

13. 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.

14. 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 The playing frequencies are a set of multiples of 116 Hz; except for the first multiple. f / integer tr 93 116

15. What if you put holes in the side of a trumpet? The result, a keyed trumpet, would have uneven tone quality.

16. Keyed bugles had a more even tone quality, but didn’t sound like trumpets.

17. Other keyed instruments met with even less success. For example, the Serpent.

18. And the Ophicleide.

19. 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? openstopped

20. http://www.phys.unsw.edu.au/jw/brassacoustics.html A good on-line reference