B Air Horn Physics: Calculating Size, Length & More for Musical Chords

[Grant M]

Hi. I am new to this forum and would like to get some information on the physics of an air horn. I am trying to design a series of air horns that each play a musical note. The problem I'm running into is what size to make each trumpet in order to produce a specific note. I know that frequency is related to length and width but I can't find an equation to use. The horns work pneumatically by a vibrating diaphragm. Ideally I'd like to use one specific dimension for the base of the bell and just vary the length to change the pitch.

I am looking for the following info:
-Calculating the total length of a horn from frequency
-The best shape of bell to use for a horn for harmonics (equation for the exponential horn bell)
-Calculating the size based on a 5" diaphragm
-other factors that I should take into consideration

The purpose of this project is to create a line of locomotive horns that play musical chords. Each set of horns will include 3-5 trumpets and must produce 96-110dB at 100ft.

Thanks for your help on this. :)

 

[Simon Bridge]

The physics is not simple ... though the fundamental is mainly to do with the tube length. The flair at the end is mainly for amplification.
The specifics of the shape give you the type of sound.

 

[anorlunda]

The mathematics of pipe organ sound https://math.dartmouth.edu/archive/m5f11/public_html/proj/Griffith.pdf
I think pipe organs and air horns are pretty much alike.

 

[Cutter Ketch]

The physics is not simple ... though the fundamental is mainly to do with the tube length. The flair at the end is mainly for amplification.
The specifics of the shape give you the type of sound.

Or perhaps the simple physics isn't close enough to right?

Try this:

https://www.grc.com/acoustics/an-introduction-to-horn-theory.pdf

But you may not like it!

 

[Grant M]

Or perhaps the simple physics isn't close enough to right?

Try this:

https://www.grc.com/acoustics/an-introduction-to-horn-theory.pdf

But you may not like it!

This PDF seems to be more of an speaker horn rather than a brass instrument. I need to figure out how to calculate the natural frequency of a horn from the dimensions. These air horns operate on basically the same principle as a trombone except with a diaphragm producing the vibration.

 

[Jayson P]

Grant, did you find the information you needed? I would love to know how your project is going. This idea has been a decades-long interest of mine.

 

[sophiecentaur]

I think pipe organs and air horns are pretty much alike.

I think the Vox Humana pipe in an organ is the most like an air horn. A reed is used at the end of a pipe. But the pipes are not tapered so they don't have a wide band match, like a tapered horn and the higher harmonics / overtones are not as pronounced as with an air horn.