When driving a car with an open window one can hear (and feel) oscillations of air at the threshold of the open window. I used to think the open window and the car interior were forming a Helmholtz oscillator, but then noticed that the frequency of the vibration doesn't change when I change scroll the window up or down, from wide open to 3/4 closed. The amplitude of vibration changes, but the frequency change I don't notice. Thus the two-part question: what causes air to vibrate in the open window? And why doesn't the frequency change when I open the window further?
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A helmholtz resonator consists of a compliance (the compressibility of an air-filled cavity) with an inertance in series (the inertia of the air in the "neck"). resonance happens when the inertance of the neck couples to the compliance of the cavity in the presence of some forcing function which contains a frequency component close to the system's natural resonant frequency. we then expect the car to behave as a helmholtz resonator where the interior volume of the car is the compliance, the mass of the air entrained in the window opening is the inertance, and the random acoustic noise generated by the air passing by is the forcing function.
The inertance of the entrained air mass in a pipe scales as (density of air) x (length of pipe)/(cross-sectional area) (I know this is counterintuitive; see Karnopp & Rosenberg, System Dynamics: A Unified Approach for the derivation). In this case the pipe length is the thickness of the window opening (which is very small compared to the compliance of the air entrained inside the car's interior) which yields a small mass bouncing on top of a soft compliance. Rolling the window up magnifies the mass effect and adds parasitic resistance so the anticipated effect would then be a lowering of the resonant frequency accompanied by a decrease in the sharpness of the resonance.
On the other hand, the car's interior may be self-resonant in the sense that the mass effect is distributed throughout the car's interior rather than being lumped in the window opening. this complicates the analysis significantly but would neatly account for the absence of an effect on the resonance with changing the size of the window opening.
Therefore, the fact that you did not experience a frequency shift in your experiments suggests either 1) the inertance is distributed and not lumped as outlined above, 2) the retuning we expect with closing the window is swamped by the added resistance, so the apparent resonant frequency does not change much, or 3) that the resonance in your car is being dominated by something other than helmholtz effects. It may be that the noise source from which the resonator selects its favored frequency is not random, but contains a component which drives the resonator strongly enough to overcome the tuning change with window adjustment.
One possible source of nonrandom noise in the airstream flowing past the car window is vortex shedding at the edge of the windshield. This can be tested experimentally by changing your airspeed, which will change the vortex shedding frequency. Try and see if the resonance inside the car shifts with the speed of the car.
niels nielsen
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