In September 2017, I attended the 20th International Conference on Digital Audio Effects in Edinburgh. At this conference, I presented my work on a real-time physically derived model of a cavity tone. The cavity tone is one of the fundamental aeroacoustic sounds, similar to previously described Aeolian tone. The cavity tone commonly occurs in aircraft when opening bomb bay doors or by the cavities left when the landing gear is extended. Another example of the cavity tone can be seen when swinging a sword with a grooved profile.
The physics of operation is a can be a little complicated. To try and keep it simple, air flows over the cavity and comes into contact with air at a different velocity within the cavity. The movement of air at one speed over air at another cause what’s known as shear layer between the two. The shear layer is unstable and flaps against the trailing edge of the cavity causing a pressure pulse. The pressure pulse travels back upstream to the leading edge and re-enforces the instability. This causes a feedback loop which will occur at set frequencies. Away from the cavity the pressure pulse will be heard as an acoustic tone – the cavity tone!
A diagram of this is shown below:
Like the previously described Aeolian tone, there are equations to derive the frequency of the cavity tone. This is based on the length of the cavity and the airspeed. There are a number of modes of operation, usually ranging from 1 – 4. The acoustic intensity has also been defined which is based on airspeed, position of the listener and geometry of the cavity.
The implementation of an individual mode cavity tone is shown in the figure below. The Reynolds number is a dimensionless measure of the ratio between the inertia and viscous force in the flow and Q relates to the bandwidth of the passband of the bandpass filter.
Comparing our model’s average frequency prediction to published results we found it was 0.3% lower than theoretical frequencies, 2.0% lower than computed frequencies and 6.4% lower than measured frequencies. A copy of the pure data synthesis model can be downloaded here.