Questions about the physics of the trumpet

[keigoh]

I have a few questions about the physics of the trumpet.

1) How does the tension on the embouchure change the resonance frequency of the horn?

I understand that the trumpet tone is created by a standing wave created by the horn. Specifically, when a sound is initiated, the acoustical properties of the trumpet and atmospheric pressure, provide a reflection or feedback of a pressure wave which then sets the lip tissue into vibration.

I also know that the frequency is determined by the alternating air current thru the Horgan, and not the pulsing of the lips.

How then, does the tension of the lips, or aperture, change the pitch of the note played?

2) When playing high notes, what is the effect of the air suppled to the horn?

I read somewhere that when playing high notes, the aperture gets small and tight fue to the added tension on the embouchure, and thus increasing the air pressure. Does this mean that we need to push more from the lungs to supoly more pressure to the air to play high notes, or you just need to release the air as you would do with the low notes, because the tension-added embouchure adds pressure to the air?

 

[Simon Bridge]

I have a few questions about the physics of the trumpet.

1) How does the tension on the embouchure change the resonance frequency of the horn?

The embouchure is the use of facial muscles and the shaping of the lips to the mouthpiece of woodwind instruments or the mouthpiece of the brass instruments.

I would not expect this to have any effect on the resonant frequency of the trumpet.
The tone produced depends mainly on the length of the pipe.

When you blow into the trumpet, you are basically making a farting noise (sort of) which drives the trumpet. How you hold your mouth etc and blow affects the strength and frequency-mix of this driving signal. The driving frequency needs to be close to the trumpets resonant frequency in order to produce a loud tone.

The driving signal will have a mix of tones in it - it's pretty discordant by itself. The trumpet selectively amplifies those tones close to the resonant frequency.

2) When playing high notes, what is the effect of the air suppled to the horn?

I read somewhere that when playing high notes, the aperture gets small and tight fue to the added tension on the embouchure, and thus increasing the air pressure. Does this mean that we need to push more from the lungs to supoly more pressure to the air to play high notes, or you just need to release the air as you would do with the low notes, because the tension-added embouchure adds pressure to the air?

Off the previous answer - if you tighten up, the farting" driving signal gets higher pitched too. You need to do this to get the frequency of the driving signal closer to the resonant frequency of the trumpet.

High notes are also high-energy notes so you need higher pressure to drive them.

 

[Andy Resnick]

I have a few questions about the physics of the trumpet.

These are good questions; the physics of brass instruments is fairly complex. Even worse, the physics-oriented "physics of music" texts are often not written by expert players: my neighbor is a professional horn player, and he has demonstrated to me a lot of phenomena that the books either ignore, are ignorant of, or even claim to be impossible. For example, he once played a 2-octave slide on a french horn without fingering anything- he modulated his mouth only.

Adding an embouchure to a straight tube alters the resonant frequency in subtle ways. For low resonances, there is no shift in lower frequencies but the upper resonances are shifted down as the mouth + cup are also a resonant system. The bell also shifts resonance frequencies, but this effect is to raise the lower resonances and leave the upper resonances unaffected.

As for generating the tone, you are correct that a resonance is set up along the entire length of the tube, including the mouth, and modulating the mouth results in modulating the tone (so does modulating the length of the tube). This is where my neighbor's knowledge far exceeds my understanding- he can adjust not just the tone itself, but the attack and other dynamic parameters of the note with mouth and tongue movements. He doesn't 'blow' exactly, not like blowing up a balloon, it's more of a feedback interaction where he just maintains the note, which does not require much 'blowing'. I don't know how long he could hold a note for.

When he plays higher notes it's clear his mouth is 'tighter', but I don't know if he is modulating the pressure or for example, keeping his mouth more rigid- like I said, his knowledge far exceeds my understanding.

Do you play trumpet or other instrument?

 

[keigoh]

Yes, I have been playing the trumpet for a few years.

I find that the higher notes require as much air pressure from the lungs as the lower notes; the only difference is in the embouchure.

 

[Simon Bridge]

Andy is correct that the physics is very complex - I still think the mouth+trumpet are better understood as coupled resonators. There are a bunch of subtleties I didn't cover in post #2.

You can work out the energy density in low vs high notes for yourself - the energy has to come from someplace.
OTOH: you'll have noticed that in some instruments (i.e. recorder) you have to blow more softly for the higher notes or you'll not get a nice sounding note. You can drive a lower amplitude signal and rely on the resonance to pick the volume up but you'll notice that the higher notes sound "softer".

 

[sophiecentaur]

You can use a trumpet mouthpiece on its own and produce a continuous range of frequencies. The air column in the trumpet acts like a filter with many peaks and nulls. If you blow a rasberry with an appropriate frequency, you get a 'good' note with little effort. (Higher frequency means harder work, though).
The filter characteristic of the air column is not 'high Q' and you can force notes through which don't correspond to natural resonance peaks. The skilled horn player was doing this but the notes, produced wouldn't have sounded as nice and would probably not have been as loud.
I did learn the trumpet briefly and I can remember that you could 'relax' your lips once you actually found the right note for the valve setting. This is where the sound power is being 'matched' into the air. You could feel the resonance working.