1. The Physics of Brass Musical Instruments Or, what do horn players do with their right hands, anyway? Brian Holmes, Department of Physics, San Jose State University

2. The Physics of Brass Musical Instruments Or, what do horn players do with their right hands, anyway? (while playing the horn) Brian Holmes, Department of Physics, San Jose State University

3. Intended structure of this talk Standing waves on strings and in tubes. How to build a trumpet. What horn players do with their right hands, anyway.

4. Actual structure of this talk Two skits. A digression. Another digression (if time allows). A lot of rushing toward the end as I try to leave out a lot of information I nearly included.

5. 79 181 304 428 545 670 Playing frequencies of straight tube Length: 1.41m cyl f Frequencies are in cycles per second

6. 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

7. 79 181 304 428 545 670 What happens when you add the bell f cyl f bell 93 221 334 449 574 691

8. 79 181 304 428 545 670 What happens when you add the bell: the frequencies rise. f cyl f bell 93 221 334 449 571 691 ff 14 40 30 21 26 21

9. 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.

10. 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 cutoff frequency, little sound is reflected back to the lips. The cutoff frequency is higher for a more rapidly flaring bell.

11. This is why brass instruments, unlike woodwinds, use valves (or slides) instead of side holes.

12. Keyed trumpet Keyed Bugle

13. Mouthpiece 5 = cup 7 = backbore

14. The mouthpiece has a cup-shaped bowl. This gives it 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.

15. 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.

16. 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 now a set of all multiples of 116 Hz; except for the first multiple. f / integer tr 93 116

17. 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?