Whistle Components
The whistles have three main components. The aperture, bell, and resonator.
Aperture
The aperture is responsible for creating a thin curtain of fluid that impacts the edges of the bell mouth. The aperture assembly produces a circular fluid curtain by allowing the fluid to pass through a narrow gap. The gap dimension is 0.0065 inch. It is critical for good operation of the whistle that the aperture gap be even or symmetrical all around the aperture. The two parts that are used to construct a Bangham whistle aperture assembly for Gauge 1 sized whistles are produced on commercial CNC Swiss lathes to maintain tolerance on the width of the gap when the parts are assembled into an aperture assembly.Bell
The bell was previously referred to as the resonator tube (SITG #66). Larry has decided that it really functions as the bell on a prototype whistle and should be called such. This portion is the neck section of the Helmholtz Resonator. Either way, the part of the bell that the jet of steam from the aperture strikes is the mouth. After the jet strikes the mouth, the bell can either go straight or have an angle put into it.
The actual realized physical length of the bell is interdependent upon the frequency desired, and the volume of the resonator. This has to be calculated using the Helmholtz formula.
The maximum total length of the bell is ten times the inside diameter (ID) of the bell. This works out to 1.6 inches (40.64 mm) when using the currently standard 0.1875 (3/16) outside diameter, 0.014 wall, .159 inside diameter Brass tubing. This length is inclusive of any bends, and parts inserted into the resonator cavity. The minimum length is usually dependent upon mechanical mounting concerns for attaching the aperture assembly to the bell.
Resonator
The magic thing that makes it work. Actually, it's proper name including the bell is "Helmholtz Resonator". Stick that in Google and have fun.
The resonator can take many shapes, normally sticking with tubular and rectangular sections since they are easier to fabricate. The resonator also has been made in "C" shapes for inclusion in dome style whistles.
Tuning or Sizing the Bell and Resonator
The Helmholtz resonator formula determines the sizing of the bell and resonator. The formula requires the inside diameter of the neck, the neck length, and the resonator volume. I found that creating a Microsoft Excel sheet and utilizing the solver function was the easiest way to get the dimensioning of the various parts. Also, it is easier to let the computer figure out a square root.
Helmholtz Formula by Larry Bangham in SITG #67 rephrased
freq = K * SQRT( (Aperture Area / Resonator Volume ) * ( Bell length + (( .96 * Aperture Area) / 2)) ) )
Where K = Speed of sound in air / 2pi = 2156 for air
I'm going to be adding a calculator page for this at some point in the future.