Resonance in Air Cavities

The large bottle is composed of a main cylinder that is 8.75 in diameter and 12 tall (we re using inches here because the fluid volume is expressed in gallons normally we d try to use meters and liters). A cone atop the cylinder rises for about 3, then joins a small cylindrical neck which is 2 tall and 1.5 in diameter. The little bottle is a cylinder 2.375 tall and 1.125 in diameter. 

Figare 11.7. Three gallon water bottle model. 

The end correction factor means that we wouldn t really need a pipe attached to the volume cavity to make a resonator. Just drilling a hole in the wall of a cavity will cause it to behave like a resonator. One big low resonance of an acoustic guitar is a Helmholtz resonance due to the cavity of the body and the sound hole. 

Although extremely simple, the low dimensional models of air-based resonators presented in this chapter capture remarkable amoimts of the behavior of such systems. More refinements can be made if needed, but much open research remains to be done in the area of the effects and computation of fluid dynamics in wind-based sound producers. In the next chapter, we will tmn back to solid resonators, looking at higher dimensional systems. 

McIntyre, R. T. Schumacher, and J. Woodhouse. On the Oscillations of Musical Instruments. Journal of the Acoustic Society of America 74(5) 1325—1345 (1983). 

---