Another in our continuing exploration of everyday sounds (Screams, Applause, Pouring water) is the bouncing ball. It’s a nice one for a blog entry since there are only a small number of papers focused on bouncing, which means we can give a good overview of the field. It’s also one of those sounds that we can identify very clearly; we all know it when we hear it. It has two components that can be treated separately; the sound of a single bounce and the timing between bounces.
Let’s consider the second aspect. If we drop a ball from a certain height and ignore any drag, the time it takes to hit the ground is completely determined by gravity. When it hits the ground, some energy is absorbed on impact. And so it may be traveling downwards with a velocity v1 just before impact, and after impact travels upwards with velocity v2. The ratio v2/v1 is called the coefficient of restitution (COR). A high COR means that the ball travels back up almost to its original height, and a low COR means that most energy is absorbed and it only travels up a short distance.
Knowing COR, one can use simple equations of motion to determine the time between each bounce. And since the sum of the times between bounces is a convergent series, one can find the maximum time until it stops bouncing. Conversely, measuring the coefficient of friction from times between bounces is literally a tabletop physics experiment (Aguiar 2003, Farkas 2006, Schwarz 2013). And kinetic energy depends on the square of the velocity, so we know how much energy is lost with each bounce, which also gives an idea of how the sound levels of successive bounces should decrease.
[The derivation of all this has been left to the reader 😊. But again, its straightforward application of the equations of motion that give time dependence of position and velocity under constant acceleration]
Its not that hard to extend this approach, for instance by including air drag or sloped surfaces. But if you put the ball on a vibrating platform, all sorts of wonderful nonlinear behaviour can be observed; chaos, locking and chattering (Luck 1993).
For instance, have a look at the following video; which shows some interesting behaviour where bouncing balls all seem to organise onto one side of a partition.
So much for the timing of bounces, but what about the sound of a single bounce? Well, Nagurka (2004) modelled the bounce as a mass-spring-damper system, giving the time of contact for each bounce. It provides a little more realism by capturing some aspects of the bounce sound, Stoelinga (2007) did a detailed analysis of bouncing and rolling sounds. It has a wealth of useful information, and deep insights into both the physics and perception of bouncing, but stops short of describing how to synthesize a bounce.
To really capture the sound of a bounce, something like modal synthesis should be used. That is, one should identify the modes that are excited for impact of a given ball on a given surface, and their decay rates. Farnell measured these modes for some materials, and used those values to synthesize bounces in Designing Sound . But perhaps the most detailed analysis and generation of such sounds, at least as far as I’m aware, is in the work of Davide Rocchesso and his colleagues, leaders in the field of sound synthesis and sound design. They have produced a wealth of useful work in the area, but an excellent starting point is The Sounding Object.
Are you aware of any other interesting research about the sound of bouncing? Let us know.
Next week, I’ll continue talking about bouncing sounds with discussion of ‘the audiovisual bounce-inducing effect.’
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
The Heyser lecture is a distinguished talk given at each AES Convention by eminent individuals in audio engineering and related fields. At the 140th AES Convention, Rozenn Nicol was the Heyser lecturer. This was well-deserved, and she has made major contributions to the field of immersive audio. But what was shocking about this is that she is the first woman Heyser lecturer. Its an indicator that woman are under-represented and under-recognised in the field. With that in mind, I’d like to highlight some women who have made major contributions to the field, especially in research and innovation.
The Eidophone, demonstrated by Grace Digney.
Do you know some others who should be mentioned? We’d love to hear your thoughts.
And check out Women in Audio: contributions and challenges in music
technology and production for a detailed analysis of the current state of the field.
At the recent Audio Engineering Society Convention, one of the most interesting talks was in the E-Briefs sessions. These are usually short presentations, dealing with late-breaking research results, work in progress, or engineering reports. The work, by Charalampos Papadokos presented an e-brief titled ‘Power Out of Thin Air: Harvesting of Acoustic Energy’.
Ambient energy sources are those sources all around us, like solar and kinetic energy. Energy harvesting is the capture and storage of ambient energy. It’s not a new concept at all, and dates back to the windmill and the waterwheel. Ambient power has been collected from electromagnetic radiation since the invention of crystal radios by Sir Jagadish Chandra Bose, a true renaissance man who made important contributions to many fields. But nowadays, people are looking for energy harvesting from many more possible sources, often for powering small devices, like wearable electronics and wireless sensor networks. The big advantages, of course, is that energy harvesters do not consume resources like oil or coal, and energy harvesting might enable some devices to operate almost indefinitely.
But two of the main challenges is that many ambient energy sources are very low power, and the harvesting may be difficult.
Typical power densities from energy harvesting can vary over orders of magnitude. Here’s the energy densities for various ambient sources, taken from the Open Access book chapter ‘Electrostatic Conversion for Vibration Energy Harvesting‘ by S. Boisseau, G. Despesse and B. Ahmed Seddik ‘.
You can see that vibration, which includes acoustic vibrations, has about 1/100th the energy density of solar power, or even less. The numbers are arguable, but at first glance it looks like it will be exceedingly difficult to get any significant energy from acoustic sources unless one can harvest over a very large area.
That’s where this e-brief paper comes in. Papadokos and his co-author, John Mourjopoulos, have a patented approach to harvesting the acoustic energy inside a loudspeaker enclosure. Others had considered harvesting the sound energy from loudspeakers before (see the work of Matsuda, for instance), but mainly just as a way of testing their harvesting approach, and not really exploiting the properties of loudspeakers. Papadokos and Mourjopoulos had the insight to realise that many loudspeakers are enclosed and the enclosure has abundant acoustic energy that might be harvested without interfering with the external design and without interfering with the sound presented to the listener. In earlier work, Papadokos and Mourjopoulos found that sound pressure within the enclosure often exceeds 130 dBs within a loudspeaker enclosure. Here, they simulated the effect of a piezoelectric plate in the enclosure, to convert the acoustic energy to electrical energy. Results showed that it might be possible to generate 2.6 volts under regular operating conditions, thus proving the concept of harvesting acoustic energy from loudspeaker enclosures, at least in simulation.
Sonic weapons frequently occur in science fiction and fantasy. I remember reading the Tintin book The Calculus affair, where Professor Calculus invents ultrasonic devices which break glass objects around the house. But the bad guys from Borduria want to make them large scale and long range devices, capable of mass destruction.
As with many fantastic fiction ideas, sonic weapons have a firm basis in fact. But one of the first planned uses for sonic devices in war was as a defense system, not a weapon.
Between about 1916 and 1936, acoustic mirrors were built and tested around the coast of England. The idea is that they could reflect, and in some cases focus, the sound of incoming enemy aircraft. Microphones could be placed at the foci of the reflectors, giving listeners a means of early detection. The mirrors were usually parabolic or spherical in shape detect the aircraft, and for the spherical designs, the microphone could be moved as a means of identifying the direction of arrival.
It was a good idea at first, but air speed of bombers and fighters improved so much over that time period that it would only give a few minutes extra warning. And then the technology became completely obsolete with the invention of radar, though that also meant that the effort into planning a network of detectors along the coast was not wasted.
The British weren’t the only ones attempting to use sound for aircraft detection between the world wars. The Japanese had mobile acoustic locators known as ‘war tubas,’ Dutch had personal horns and personal parabolas, the Czechs used a four-horn acoustic locator to detect height as well as horizontal direction, and the French physicist Jean-Baptiste Perrin designed the télésitemètre, which in a field full of unusual designs, still managed to distinguish itself by having 36 small hexagonal horns. Perrin though, is better known for his Nobel prize winning work on Brownian motion that finally confirmed the atomic theory of matter. Other well-known contributors to the field include the Austrian born ethnomusicologist Erich Moritz von Hornbo and renowned psychologist Max Wertheimer. Together, they developed the sound directional locator known as the Wertbostel, which was believed to have been commercialised during the 30s.
There are wonderful photos of these devices, most of which can be found here , but I couldn’t resist including at least a couple,
a German acoustic & optical locating apparatus, and a Japanese war tuba.
and a Japanese war tuba.
But these acoustic mirrors and related systems were all intended for defense. During World War II, German scientists worked on sonic weapons under the supervision of Albert Speer. They developed an acoustic cannon that was intended to send a deafening, focused beam of sound, magnified by parabolic reflector dishes. Research was discontinued however, since initial efforts were not successful, nor was it likely to be effective in practical situations.
Devices capable of producing especially loud sounds, often focused in a given direction or over a particular frequency range, have found quite a few uses as weapons of some kind. A long-range acoustic device was used to deter pirates who attempted to attack a cruise ship, for instance, and sonic devices emitting high frequencies that might be heard by teenagers but unlikely to be heard by adults have been deployed in city centres to prevent youth from congregating. However, such stories make for interesting reading, but it’s hard to say how effective they actually are.
And there are even sonic weapons occurring in nature.
The snapping shrimp has a claw which shoots a jet of water, which in turn generates a cavitation bubble. The bubble bursts with a snap reaching around 190 decibels. Its loud enough to kill or stun small sea creatures, who then become its prey.