The edgiest tone yet…

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. May 24th at the 144th Audio Engineering Society Convention in Milan, I will present ‘Physically Derived Synthesis Model of an Edge Tone.’
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.

 

Vertical take-off of a Harrier jet

 

The cavity tone……

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.

 

Physically Derived Sound Synthesis Model of a Propeller

I recently presented my work on the real-time sound synthesis of a propeller at the 12th International Audio Mostly Conference in London. This sound effect is a continuation of my research into aeroacoustic sounds generated by physical models; an extension of my previous work on the Aeolian harp, sword sounds and Aeolian tones.

A demo video of the propeller model attached to an aircraft object in unity is given here. I use the Unity Doppler effect which I have since discovered is not the best and adds a high-pitched artefact but you’ll get the idea! The propeller physical model was implemented in Pure Data and transferred to Unity using the Heavy compiler.

So, when I was looking for an indication of the different sound sources in a propeller sound I found an excellent paper by JE Marte and DW Kurtz. (A review of aerodynamic noise from propellers, rotors, and lift fans. Jet Propulsion Laboratory, California Institute of Technology, 1970) This paper provides a breakdown of the different sound sources, replicated for you here.

The sounds are split into periodic and broadband groups. In the periodic sounds, there are rotational sounds associated with the forces on the blade and interaction and distortion effects. The first rotational sound is the Loading sounds. These are associated with the thrust and torque of each propeller blade.

To picture these forces, imagine you are sitting on an aircraft wing, looking down the span, travelling at a fixed speed and uniform air flowing over the aerofoil. From your point of view the wing will have a lift force associated with it and a drag force. Now if we change the aircraft wing to a propeller blade with similar profile to an aerofoil, spinning at a set RPM. If you are sitting at a point on the blade the thrust and torque will be constant at the point you are sat.

Now stepping off the propeller blade and examining the disk of rotation the thrust and torque forces will appear as pulses at the blade passing frequency. For example, a propeller with 2 blades, rotating at 2400 RPM will have a blade passing frequency of 80Hz. A similar propeller with 4 blades, rotating at the same RPM will have a blade passing frequency of 160Hz.

Thickness noise is the sound generated as the blade moves the air aside when passing. This sound is found to be small when blades are moving at the speed of sound, 343 m/s, (known as a speed of Mach 1), and is not considered in our model.

Interaction and distortion effects are associated with helicopter rotors and lift fans. Because these have horizontally rotating blades an effect called blade slap occurs, where the rotating blade passes through the vortices shed by the previous blade causing a large slapping sound. Horizontal blades also have AM and FM modulated signals related with them as well as other effects. Since we are looking at propellers that spin mostly vertically, we have omitted these effects.

The broadband sounds of the propeller are closely related to the Aeolian tone models I have spoken about previously. The vortex sounds are from the vortex shedding, identical to out sword model. This difference in this case is that a propeller has a set shape which more like an aerofoil than a cylinder.

In the Aeolian tone paper, published at AES, LA, 2016, it was found that for a cylinder the frequency can be determined by an equation defined by Strouhal. The ratio of the diameter, frequency and airspeed are related by the Strouhal number, found for a cylinder to be approximately 0.2. In the paper D Brown and JB Ollerhead, Propeller noise at low tip speeds. Technical report, DTIC Document, 1971, a Strouhal number of 0.85 was found for propellers. This was used in our model, along with the chord length of the propeller instead of the diameter.

We also include the wake sound in the Aeolian tone model which is similar to the turbulence sounds. These are only noticeable at high speeds.

The paper by Martz et. al. outlines a procedure by Hamilton Standard, a propeller manufacturer, for predicting the far field loading sounds. Along with the RPM, number of blades, distance, azimuth angle we need the blade diameter, and engine power. We first decided which aircraft we were going to model. This was determined by the fact that we wanted to carry out a perceptual test and had a limited number of clips of known aircraft.

We settled on a Hercules C130, Boeing B17 Flying Fortress, Tiger Moth, Yak-52, Cessna 340 and a P51 Mustang. The internet was searched for details like blade size, blade profile (to calculate chord lengths along the span of the blade), engine power, top speed and maximum RPM. This gave enough information for the models to be created in pure data and the sound effect to be as realistic as possible.

This enables us to calculate the loading sounds and broadband vortex sounds, adding in a Doppler effect for realism. What was missing is an engine sound – the aeroacoustic sounds will not happen in isolation in our model. To rectify this a model from Andy Farnell’s Designing Sound was modified to act as our engine sound.

A copy of the pure data software can be downloaded from this site, https://code.soundsoftware.ac.uk/hg/propeller-model. We performed listening tests on all the models, comparing them with an alternative synthesis model (SMS) and the real recordings we had. The tests highlighted that the real sounds are still the most plausible but our model performed as well as the alternative synthesis method. This is a great result considering the alternative method starts with a real recording of a propeller, analyses it and re-synthesizes it. Our model starts with real world physical parameters like the blade profile, engine power, distance and azimuth angles to produce the sound effect.

An example of the propeller sound effect is mixed into this famous scene from North by Northwest. As you can hear the effect still has some way to go to be as good as the original but this physical model is the first step in incorporating fluid dynamics of a propeller into the synthesis process.

From the editor: Check out all Rod’s videos at https://www.youtube.com/channel/UCIB4yxyZcndt06quMulIpsQ

A copy the paper published at Audio Mostly 2017 can be found here >> Propeller_AuthorsVersion