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The resonance of woodwind brass instruments can be modeled after a closed cylindrical pipe and calculated by the equation f = (nv)/(4L) where n denotes the number of harmonics, v the velocity of sound propagating in air, and L the length of the pipe. For a trumpet that has tube length of about 1.4m, the resonating frequencies would be:

f = (nv)/(4L) = (343n)/(4*1.4) = 61.3n = 61Hz, 184Hz, 306Hz, 429Hz...

The sound of a trumpet ranges from [email protected] up to [email protected]. I tried as hard as I can vibrating (buzzing) my lips, but I can hardly get my mouth to vibrate more than perhaps a few tens Hz without getting sore. It's hard to believe, even with practice, that a person can possibly vibrate his lips hundreds of Hertz, let alone over a 1000Hz (or do they?).

Do woodwind brass instrument players really vibrate their lips as quickly as the pipe resonates?

KMC
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    The players might not be able to vibrate that fast, but the instrument might interact with the lips (kind of a feedback loop) to make this happen. Note that the trumpet is not a woodwind. – Tom Jul 08 '21 at 06:38
  • The given hertz figures don't match those [here](https://pages.mtu.edu/~suits/notefreqs.html), but are in the correct order of magnitude. – guidot Jul 08 '21 at 07:03
  • @Tom you're right. Brass, not woodwind. Question amended. – KMC Jul 08 '21 at 08:33
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    A closed cylindrical pipe only produces odd-numbered harmonics. The bell flare and the mouthpiece together allow a trumpet to produce all the harmonic series, not just the odd-numbered ones. – Brian THOMAS Jul 08 '21 at 11:52

2 Answers2

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At least for trumpet, yes, the lips really vibrate that quickly.

For a high trumpet note, the lips may vibrate at more than 1000 vibrations per second. This is fast, but remember that the muscles are not contracting at that rate: the muscles in the brass player's lips exert almost constant tension, and it is the elastic and aerodynamic forces on the lips that produce the vibration. (SOURCE: this site also has pages devoted to various woodwinds, so you may find similar information there.)

Trumpet players often practice "buzzing" our lips on various pitches — for example, playing a scale lips only (we also do the same kind of practice mouthpiece only). The trumpet becomes a tool to focus that sound. However, this can be quite difficult and take significant practice. It's generally easier to form pitches with the trumpet than without, but even with, it can take years to develop the ability to play higher pitches.

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Aaron
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  • Just mind boggling to know that the lips can vibrate that quickly without damaging the soft tissues – KMC Jul 08 '21 at 07:14
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    Maynard Ferguson! :-) – Carl Witthoft Jul 08 '21 at 17:38
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    @KMC I wouldn't say there's *no* damage. From my limited time with the trumpet, I can say that your lips can *hurt* after playing for a while. This is one of the reasons I gave up playing it after a few years. I imagine professionals build up tolerance for that, but I never got there. (I'll stick with the piano, thank you very much.) – Darrel Hoffman Jul 08 '21 at 20:30
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    Come to that, as my son has just pointed out, the vocal cords also have to vibrate pretty fast, which does not seem to surprise the questioner as much! – PJTraill Jul 08 '21 at 21:43
  • @DarrelHoffman good to get a perspective of an actual trumpet player and I know none of them. A great point PJTriall brought up - I guess a slight difference in that is when I tried buzzing as quick a I can I can't help but kept spitting all over the place so at 1000Hz my mouth would basically split like machine gun which is physically impossible if I image. But like Tom comment mentioned, there's some feedback mechanism that opens my mouth without needing the player exerting all the muscular force of splitting air (or saliva in my case) constantly at that frequency. – KMC Jul 09 '21 at 03:57
  • @KMC when developing endurance for trumpet, you develop both the muscles that support the embouchure, but also the ability for your lips to withstand playing for extended periods. Those both usually improve together, but depending on what you’re doing, you can reach the limit of one or the other. For the former, it’s just soreness/cramping of the cheeks, for the latter, the soft tissue of the lips definitely begins to hurt. As an aside, if you try “buzzing” into an opening that you make with your fingers you can get much higher pitches more easily and is akin (though not quite) to a mouthpiece – fyrepenguin Jul 09 '21 at 05:21
  • If your lips hurt, then you probably are not providing enough diaphragmatic breath control (leaving out beginner students here). The more work your thorax muscles do, the less stress on those in your mouth. – Carl Witthoft Jul 09 '21 at 11:19
  • @kmc "I can't help but kept spitting all over the place" - And now you know why trumpets have spit valves! But seriously, did you try buzzing your lips in air or with a mouthpiece? It is easier to do with a mouthpiece. – Glen Yates Jul 09 '21 at 13:05
  • @KMC Very much an *ex*-trumpet player. I only played for a few years in middle school, a *long* time ago. I'm sure there are many people on this site with more recent and professional experience. – Darrel Hoffman Jul 09 '21 at 13:12
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    Vocal cords, as @PJTraill mentions, are a very apt comparison. The muscles don’t themselves vibrate the lips or vocal cords at 1000Hz (or whatever frequency). They *tense* the lips/cords, and then the airflow causes the tensed surfaces to vibrate. Whatever fatigue/pain occurs is not caused by the vibration, but by the tension. – PLL Jul 09 '21 at 15:25
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Yes, the lips really do vibrate at that frequency. Any material or object can vibrate at pretty much any frequency, if they're driven at that frequency. For example, when you get a medical ultrasound, your body tissues are vibrating at something like 100-1000 kHz.

Your physical intuition is being misled by the fact that your body's frequencies of free vibration are more specific and limited. For example, if you sit perched on a high stool and swing your leg like a pendulum, its frequency will be on the order of 1 Hz. Dogs pant at the natural frequency of their chest and diaphragm, which is on the order of 10 Hz.

In the case of the trumpet, the frequency of free vibration isn't what's relevant. The lips are strongly coupled to the air column of the trumpet. The harmonic frequencies of the air column are the ones at which the lips get driven.

  • According to google, medical ultrasound is in the range 2-18 MHz – Brian THOMAS Jul 09 '21 at 11:46
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    Curious what you mean by “dogs pant at the natural frequency of their chest and diaphragm, which is on the order of 10Hz.” It gives me a mental picture of a dog inhaling and exhaling ten times a second, which is much faster than my observations. A random chihuahua video I found on Youtube shows panting at maybe 4Hz. – Jacob Krall Jul 09 '21 at 15:34