As my PhD is coming to an end and the writing phase is getting more intense, it seemed about time I described the last of the aeroacoustic sounds I have implemented as a sound effect model. The edge tone is the sound created when a planar jet of air strikes an edge or wedge.
The edge tone is probably most often seen as means of excitation for flue instruments. These instruments are ones like a recorder, piccolo, flute and pipe organ. For example, in a recorder air is blown by the mouth through a mouthpiece into a planar jet and then onto a wedge. The forces generated couple with the tube body of the recorder and a tone based on the dimension of the tube is generated.
Mouthpiece of a recorder
The edge tone model I have developed is viewed in isolation rather than coupled to a resonator as in the musical instruments example. While researching the edge tone it seemed clear to me that this tone has not had the same attention as the Aeolian tone I have previously modelled (here) but a volume of research and data was available to help understand and develop this model.
How does the edge tone work?
The most important process in generating the edge tone is the set up of a feedback loop from the nozzle exit to the wedge. This is similar to the process that generates the cavity tone which I discussed here. The diagram below will help with the explanation.
Illustration of jet of air striking a wedge
The air comes out of the nozzle and travels towards the wedge. A jet of air naturally has some instabilities which are magnified as the jet travels and reaches the wedge. At the wedge, vortices are shed on opposite sides of the wedge and an oscillating pressure pulse is generated. The pressure pulse travels back towards the nozzle and re-enforces the instabilities. At the correct frequency (wavelength) a feedback loop is created and a strong discrete tone can be heard.
To make the edge tone more complicated, if the air speed is varied or the distance between the nozzle exit to the wedge is varies, different modes exist. The values at which the modes change also exhibit hysteresis – the mode changes up and down do not occur at the same airspeed or distance.
Creating a synthesis model
There are a number of equations defined by researchers from the fluid dynamics field, each unique but depend on an integer mode number. Nowhere in my search did I find a method of predicting the mode number. Unlike previous modelling approaches, I decided to collate all the results I had where the mode number was given, both wind tunnel measurements and computational simulations. These were then input to the Weka machine learning workbench and a decision tree was devised. This was then implemented to predict the mode number.
All the prediction equations had a significant error compared to the measured and simulated results so again the results were used to create a new equation to predict the frequency for each mode.
With the mode predicted and the subsequent frequency predicted, the actual sound synthesis was generated by noise shaping with a white noise source and a bandpass filter. The Q value for the filter was unknown but, as with the cavity tone, it is known that the more turbulent the flow the smaller and more diffuse the vortices and the wider the band of frequencies around the predicted edge tone is. The Q value for the bandpass was set to be proportional to this.
And what next…?
Unlike the Aeolian tone where I was able to create a number of sound effects, the edge tone has not yet been implemented into a wider model. This is due to time rather than anything else. One area of further development which would be of great interest would be to couple the edge tone model to a resonator to emulate a musical instrument. Some previous synthesis models use a white noise source and an excitation or a signal based on the residual between an actual sample and the model of the resonator.
Once a standing wave has been established in the resonator, the edge tone locks in at that frequency rather than the one predicted in the equation. So the predicted edge tone may only be present while a musical note is in the transient state but it is known that this has a strong influence over the timbre and may have interesting results.
For an analysis of whistles and how their design affects their sound check out his article. The feedback mechanism described for the edge tone also very similar to the one that generates the hole tone. This is the discrete tone that is generated by a boiling kettle. This is usually a circular jet striking a plate with a circular hole and a feedback loop established.
Hole tone form a kettle
A very similar tone can be generated by a vertical take-off and landing vehicle when the jets from the lift fans are pointing down to the ground or deck. These are both areas for future development and where interesting sound effects could be made.