Standing Wave in Trumpet Wind Column
I have done several blogs about how a trumpet works and I have quite a few videos about it as well. As a result of communications via these blogs and discussions I have had with other trumpeters on gigs, I decided to post this short blog about standing waves and variable acoustic length. This is essentially an addendum to last weeks blog about timbre, slotting, versus mouthpieces and horns.
If you want to skip to the main theme for this week, just scroll below the review to the figure that is used in the cover page for this blog.
For a quick review, check out these previous posts.
Also, here are some videos on the basic physics of trumpet.
Overtone Series for my physics classes:
Overtone Series for my physics classes, but with PPT added:
Trumpet Physics Segment One: (more for trumpeters)
Trumpet Physics Segment Two: (again, more for trumpeters)
Now, to the new material. Last week, I got into quite a few discussions about slotting and where it ends on trumpet. You should notice that the slots tend to get so close together as to essentially disappear as you get up to around a G (concert F) above highC on your Bb trumpet. At that point the horn wind column is essentially moving into no more resonance. You can slide from that G on up with almost no slots any more, UNTIL YOU GET TO DOUBLE C, and then a slot suddenly appears.
That slot should NOT be there, but it clearly is. In last week's blog (see the link near the top) I explain my theory as to what is happening there. All I want to do HERE is explain what is happening in general.
When you play a trumpet, a standing wave forms up at the resonant notes - harmonics - you are playing on a given valve combination. There is always a pressure antinode in the mouthpiece just in front of the lips. There is always a pressure node NEAR the bell.
That last sentence is the part that might seem odd. As you play different harmonics on the horn, the last pressure node occurs in different places. I'll now speak in "Bb trumpet speak" as opposed to concert pitch.
When you play a low C, there will, of course be a pressure antinode in the mouthpiece. In the figure just above (taken from Tom Rossing's book, "The Science of Sound) he shows the first four mode (harmonics) on a trumpet wind column). The first mode would be pedal C (or close to it), the next mode would be low C. Next, would be second line G. Finally, would be the C in the staff. You'll notice that the final node for each higher and higher mode gets closer to the bell. Around a G over high C, the last node is right at the bell barrier. Above that, no more nodes and antinodes. The trumpet wind column is essentially just a megaphone.
This is why it is physically challenging to play those notes. There is no longer any resonance helping you out.
However, as I mentioned earlier (and in last week's blog), there are a few more slots around DHC, DHB, DHD, etc. Some other part of the wind column/chamber system has begun to resonate.
So, that is it for this week's science-y blog. I hope it all made some sense.
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