# Trumpet physics

by brandonc
Tags: physics, trumpet
 P: 3 I am a trumpet player at a conservatory and I've been told for years that reducing the amount of air pressure through the trumpet will increase the volume of air that flows through the instrument. The people that have told me this always cite Boyle's law, but my understanding is that Boyle's law only applies to a closed system, which a trumpet is not. So my question is, will blowing harder through a trumpet actually increase or decrease the volume of air that is moved through the horn? My own very un-scientific experiment with a plastic bag over the bell of the trumpet and a stopwatch seems to show that more pressure actually increases volume, which is the opposite of what I've always been told. Are there any laws like Boyle's law that describe the volume and pressure of air moving through an open system?
 P: 289 Before even considering Boyle's law, you should rethink what you mean by "air pressure through the trumpet." The air inside the trumpet it not always at the same pressure as the air inside your lungs. Why do you think air comes out of your lungs when you exhale? Why does CO2 escape from a pop can when it is opened? The pressure difference is what forces air to move (or more accurately, what makes it's velocity change), so if you push harder you should be able to move more air in less time. I suspect the reason musicians suggest that decreasing pressure allows you to move more volume is because you tend to tense up your embouchure and make the opening through your lips smaller. In that case, the pressure in your lungs will probably be higher just because less air can make it out of your mouth (think of the limiting case with your mouth completely closed--no air can come out and yet this has nothing to do with the pressure in your trumpet). By the way, I don't see why you can't call your experiment scientific; it could just use some improvement :)
 Mentor P: 16,385 There is a lot - and a mean a lot - of misinformation out there on how brass instruments work. Much of this is perpetuated by well-meaning teachers, who are trying to get their students to do the right thing, even if for the wrong reason. (There's even more misinformation out there about the manufacture of brass instruments, but that's a topic for another day) First, the idealization that best matches a trumpet is that of a resonating tube that is closed at both ends. Right now, you're probably thinking this is a typo, so let me say it again: closed at both ends. So to first order, the volume of air is totally irrelevant. What your air stream does is provide energy to the lips, which vibrate and drive the air column in the horn into oscillation. What happens to the air column afterwards is largely irrelevant - it's done its job. It ends up flowing through the horn, as it has nowhere else to go, but the sound production has already happened. We're also victims of our terminology. "Blowing harder" usually means "higher velocity air". The volume of air entering the trumpet per unit of time is a function of two things - the size of the aperture and the velocity of the air. Blowing harder increases the amount of air from the velocity effect, but it usually is accompanied by a restriction of the aperture, so the two effects are pushing in opposite directions. However, this is really irrelevant, because as I said above, the air flowing through the horn is virtually irrelevant as far as the sound is concerned.
 Mentor P: 22,303 Trumpet physics By the way, the relevant physics principle relating velocity and pressure isn't Boyle's law, it's Bernoulli's principle. ...and taking Vanadium's explanation further to explain what your teacher wants you to do.... Your teacher wants you to relax and not force air through your lips by straining your lips and increasing backpressure with your lungs. That's what causes the straining/forced sound people get when playing high notes. If you can relax your lips while still maintaining control, you'll get a fuller, more mellow sound (more like a french horn than a kazoo). At the same time, more relaxed/controlled lips means less restriction to the air leaving your mouth.
 P: 3 Thanks for the replies everyone! I'm in agreement that there is a lot of misinformation about brass instruments, which is why I came to a physics forum and not a trumpet forum. I believe that the statement, "blow softer," or, "blow with less air pressure," will help players because it does a lot of things like relax the shoulders and neck, decrease the aperture size, relax the tongue, etc. I also know that the only real function of the air is to set the lips into vibration and after that it doesn't really matter what it does because as far as sound production goes, the trumpet is a closed system. Maybe I should rephrase my question. Taking all human error out of the equation and assuming that the opening of the mouth stays exactly the same size, if you increase the pressure of the air in the body (blow harder) will it increase, decrease, or have no effect on the volume of air that is being moved through the trumpet? My own intuition tells me that it would increase the volume of air moved through the horn. Again, I know this has almost nothing to do with tone production, I'm just curious.
Mentor
P: 22,303
 Quote by brandonc Maybe I should rephrase my question. Taking all human error out of the equation and assuming that the opening of the mouth stays exactly the same size, if you increase the pressure of the air in the body (blow harder) will it increase, decrease, or have no effect on the volume of air that is being moved through the trumpet? My own intuition tells me that it would increase the volume of air moved through the horn.
Yes, increase. It is what Bernoulli's principle/equation tells us:
http://en.wikipedia.org/wiki/Bernoulli's_principle

Rearranging the first equation and dropping the term for gravitational-based pressure gives you this:
1/2 rho v^2 = p

Rho is the density, p is the static pressure (pressure in your lungs) and v is the velocity. So if the pressure increases, the velocity increases. And if the orifice, your lips, stays constant, the increase in velocity equates to an increase in volumetric flow rate.
 P: 3 Thanks, Russ. That is exactly the info I was looking for!

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