What is the pitch or air flow constant of a whistle?

Question

I am making a whistle capable of making any sound and/or frequency based on a specific air flow, but despite my personal goal, What is the pitch or air flow constant of a whistle?

I mean to express, at what point does a whistle reach it's limits physically? when you shrink the cavity and/or the exit hole as well as maximize flow rate, eventually it should stop producing sound right? But what controls that? the size of oxygen molecules? the roughness of the container? suppose we are in a perfect world where i have infinitely decreasing size of whistles cavities that are perfect in dimension all round, is it possible to always get a sound of some-sort? and when it does get too small, im essentially asking, what factor decides that? That's the constant im looking for. a ground number to work on to predict the sound of a whistle.

of course there will never be an exact number, but im really sure it has to do with some form of how air interacts with itself at the molecular level.

Answer 1

A whistle that produces sound waves in air is adequately modeled by the ordinary laws of acoustics and does not require consideration of anything occurring at the molecular level.

The simplest model for a whistle is the helmholtz resonator, which is an acoustic filter tuned to resonate at some frequency within the audible hearing range. when excited by a broadband noise source, it picks out the resonant frequency and strongly radiates acoustic waves at that frequency.

The physical dimensions of the resonator determine the resonant frequency via an equation the derivation of which is on line. Small dimensions yield high frequencies. The point where the whistle stops producing an audible frequency is where its resonance is above the high limit of human hearing. Note that an "ultrasonic" whistle like that can still be heard by a dog's ear, even though you cannot hear it.

The same is true for the low-frequency limit of a whistle, where the dimensions of the whistle are very large. The point where the whistle stops producing an audible frequency is where its resonance is below the low limit of human hearing. Note that a "subsonic" whistle like that can still be heard by an elephant's ear, even though you cannot hear it.