Real-Time Synthesis of an Aeolian tone

Aeroacoustics are sounds generated by objects and the air and is a unique group of sounds. Examples of these sounds are a sword swooshing through the air, jet engines, propellers as well as the wind blowing through cracks, etc.  The Aeolian tone is one of the fundamental sounds; the cavity tone and edge tone being others. When designing these sound effects we want to model these fundamental sounds. It then should be possible to make a wide range of sound effects based on these. We want the sounds to be true to the physics generating them and operate in real-time. Completed effects will be suitable for use in video games, TV, film and virtual or augmented reality.

The Aeolian tone is the sound generated when air moves past a string, cylinder or similar object. It’s the whistling noise we may hear coming from a fence in the wind or the swoosh of a sword. An Aeolian Harp is a wind instrument that has been harnessing the Aeolian tone for hundreds of years. If fact, the word Aeolian comes from the Greek god of wind Aeolus.

The physics behind this sound….

When air moves past a cylinder spirals called vortices from behind it, moving away with the air flow. The vortices build up on both sides of the cylinder and detach in an alternating sequence. We call this vortex shedding and the downstream trail of vortices, a Von Karman Vortex Street. An illustration of this is given below:

strouh2

As a vortex sheds from each side there is a change in the lift force from one side to the other. It’s the frequency of this oscillating force that is the fundamental tone frequency. The sound radiates in a direction perpendicular to the flow. There is also a smaller drag force associated with each vortex shed. It is much smaller than the lift force, twice the frequency and radiates parallel to the flow. Both the lift and drag tones have harmonics present.

Can we replicate this…?

In 1878 Vincent Strouhal realized there was a relationship between the diameter of a string, the speed it was travelling thought the air and the frequency of tone produces. We find the Strouhal number varies with the turbulence around the cylinder. Luckily, we have a parameter that represents the turbulence called the Reynolds number. It’s calculated from the viscosity, density and velocity of air, and the diameter of the string. From this we can calculate the Strouhal number and get the fundamental tone frequency.

This is the heart of our model and was the launching point for our model. Acoustic sound sources can be often represented by compact sound sources. These are monopoles, dipoles and quadrupoles. For the Aeolian tone the compact sound source is a dipole.

We have an equation for the acoustic intensity. This is proportional to airspeed to the power of 6. It also includes the relationship between the sound source and listener. The bandwidth around the fundamental tone peak is proportional to the Reynolds number. We calculate this from published experimental results.

The vortex wake acoustic intensity is also calculated. This is much lower that the tone dipole at low airspeed but is proportional to airspeed to the power of 8. There is little wake sound below the fundamental tone frequency and it decreases proportional to the frequency squared.

We use the graphical programming language Pure Data to realise the equations and relationships. A white noise source and bandpass filters can generate the tone sounds and harmonics. The wake noise is a brown noise source shaped by high pass filtering. You can get the Pure Data patch of the model by clicking here.

Our sound effect operates in real-time and is interactive. A user or game engine can adjust:

  • Airspeed
  • Diameter and length of the cylinder
  • Distance between observer and source
  • Azimuth and elevation between observer and source
  • Panning and gain

We can now use the sound source to build up further models. For example, an airspeed model that replicates the wind can reproduce the sound of wind through a fence. The swoosh of a sword is sources lines up in a row with speed adjusted to radius of the arc.

Model complete…?

Not quite. We can calculate the bandwidth of the fundamental tone but have no data for the bandwidth of harmonics. In the current model we set them at the same value. The equation of the acoustic intensity of the wake is an approximation. The equation represents the physics but is not an exact value. We have to use best judgement when scaling it to the acoustic intensity of the fundamental tone.

A string or wire has a natural vibration frequency. There is an interaction between this and the vortex shedding frequency. This modifies the sound heard by a significant factor.

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