Computational Acoustics

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Methods for computer assisted prediction of acoustics is very important to research in the field of room acoustics, and for development and design of new performance spaces. Computational capacity in computers has increased since Krokstad et al started out in the 1960’s, but so have our demands.

NURBs
The application of Non-uniform Rational B-splines in room acoustic computations was presented at a session on ISRA 2013 in Toronto.

A new software tool to facilitate NURB based geometries in acoustic design by O’Keefe et al
Learning Modern Acoustical Design from Traditional Choir Venues by J O’Keefe 02.09.2013

Auralisation

A method of aural demonstration of room acoustical predictions is the so-called auralisations. With this method the computed sound received at a given point in a computer model of a room can be listened to, given the input by simulated sources in the model. This field of computational acoustics has increased the demand for proper source data, e.g. musical instruments. In order to not affect the predicted acoustics by the acoustic environment of recorded music samples, anechoic sound recordings are often preferred. How dry do the recordings for auralization need to be? A Buen asks.

For more control of individual instruments and even directional radiation, multi-channel anechoic recordings may be used.

http://www.odeon.dk/auralisation
http://www.catt.se
http://auralization.tkk.fi (free download of multi-channel anechoic recordings)

Acoustic Visualization

An introduction to Acoustic Visualization by the audio camera is presented by the following external sources:

Acoustic Visualization: The Audio Camera

Visualizing Concert Hall Reverberation

Acoustic Image Overlay: Real time Image transfer

Visually related approach can also be found in the paper Acoustical Modelling with Sonel Mapping by Kapralos et al.

Prediction of reverberant sound

Reverberant sound affects the perception of room acoustics in many ways, and is physically very complex. For frequencies higher than the absorption-dependent Schroeder Frequency

Fc~2000·(T/V)^1/2 ~800/A^1/2 ,

where T is the reverberation time, V the volume in cubic meters, and A the total (Sabine) absorption area of the room, the reverberant sound field is dominated by conditions that can be predicted by geometrical acoustics (GA), e.g. with ray-tracing methods. This means that sound in many ways acts like light, only with slower propagation speed, and thus sound rays and sound particles can be helpful models in frequency domain and time domain respectively. In a 20.000 cubic meter hall with T~2.0s, the Schroeder frequency is 20Hz, so GA applies in the practical frequency range of most concert halls.

The factor of 2000 in the Schroeder Frequency may or may not be proper for a cross-over frequency between the high frequency (GA) region and the low frequency region. This is discussed in the akutek.info article Stochastic nature of room acoustics.

More about ray-tracing and GA in “The Early History of Ray Tracing in Room Acoustics”

For frequencies lower than Fc, modes can be expected to dominate the room acoustic conditions, thus wave acoustics must be taken more into account, especially to predict the effects of standing wave patterns (hot spots, cold spots) over the room and peaks and dips in the frequency response. In practice this is significant to recording studios and rehearsal rooms.

Reverberation time significance

The significance of reverberation time in computational acoustics should not be underestimated, as demonstrated in the papers Reverberation Time—the mother of all room acoustical parameters (presentation), and Room acoustical parameters at listeners’ ears—can preferred concert hall acoustics be explained?

Effectivity of absorption

The conclusion from the paper Diffusivity and its effect on concert hall seat absorption is presented below (click for poster version):

Different rooms have different diffusivity. Therefore, one and the same absorbing surface, e.g. concert hall seats, will in general have different effective absorption coefficients. We have to deal with three different sets of absorptions coefficients when predicting acoustics, namely the input coefficients in the prediction algorithm, the lab-test coefficients, and the in-situ coefficients.

A sound absorbing object does not have absolute absorption coefficients. There exists only relative absorption coefficients, related to the measuring conditions, whether in different laboratories, or in different halls as measured in-situ. This paper suggests a method to predict the relation between absorption coefficients. In concert hall planning this method can be used to take diffuse field differences between laboratory and a concert hall into account. (more)

Computations vs Measurements

Computations are often considered inferior to measurements. Measurements are often looked upon as reality, while predicted values are looked upon as guesswork, and so on.

However, measurements and predictions belong to different domains and their data cannot be compared without further, as demonstrated in the poster Diffusivity and its effect on concert hall seat absorption. (Full paper version).

Instead, computations, objective measurements and subjective measurements could all be considered different representations of the physical world, as suggested in the paper: Room acoustical parameters at listeners’ ears—can preferred concert hall acoustics be explained?. Whenever field measured data is not a primary goal, e.g. prediction and explanation of preference and subjective quality, computational acoustics may provide a more direct method. In these cases, field measured values might as well introduce another link in a chain of uncertainties.

Handling of uncertainties and chains of uncertainties are discussed in the paper Prediction tools in acoustics—can we trust the PC?.

The apparent failure of computations is often a result of assuming computations to be an attempt to predict measured values. While sometimes the goal for computations indeed is to predict measurement values, e.g. in order to verify a prediction model, this is not always the case. In acoustics, very often the main goal is to predict experienced conditions or perceived acoustical quality, not the physical measurement data in themselves.

Measurements can provide information of controlled accuracy, however about a restricted part of the physical world. Restrictions will be defined by the measurement conditions and the actual selection of measurement points, time, frequency, and so on. Measurement data can be used to calibrate computer models. Measurements are indeed simplifications of the physical world. Measurements in empty chairs are not equal to measurements in occupied seats. Measurement data must not be confused with the physical world itself. Only approximations to the physical world is possible.

Alternative views of the relationship between measurements, computations, predictions, models, perception, subjective experience and the physical world that may be helpful:

· Computations are measurements on mathematical models (from simple formulae to complex computer assisted simulations), with varying degree of complexity and simplification

· Computations, field measurements, measurements on scale models, measured sensory impressions, measurements of perception (listening experiments, questionnaires, etc), are all being measurements with restricted validity due to selection and simplification

· All measurements are filtered representations of the physical world, thus approximations to the real world

Even in cases where field measurements are possible, e.g. when predicting annoyance from outdoor environmental noise in a residential area, computation methods may provide more reliable results, due to complexity and long-term statistical variation of the acoustic conditions, and the fact that the subjective response associated with field measurements are uncertain. This may as well be the case when dealing with experienced acoustical conditions and listening quality.

One should not forget that between the extremes of pure field measurements and pure computations there are numerous of hybrid methods, combining field data and computations.

An uncertainty chain analogy

By analogy to solar systems the relationship between physical world, measurements, computations, and subjective response can be illustrated as follows. Let physical measurements and subjective response relate to the physical world as two orbiting planets relate to the sun. Orbital radius represents the uncertainty. While physical measurements and subjective response each have direct relationships to the physical world, they relate to one another only in very complex and indirect ways. A prediction model is like a moon orbiting the planet we want to predict, e.g. the moon called Odeon orbiting the planet called Measured G. Even if the moon is relatively close to the planet (uncertainty is small), it introduces yet another link in the uncertainty chain: Moon to Planet A; Planet A to Sun; Sun to Planet B. In our analogy the uncertainty chain is made up by these links: Odeon to Measured G; Measured G to Physical World; Physical World to Subjective Response. If we discovered a moon orbiting not too far from the dark planet called Subjective Response, this moon would provide a more accurate prediction of Subjective Response than by first observing a moon orbiting Measured G. In similar way, a prediction model of subjective response could be less uncertain than combining a prediction of objective response with some correlation between objective response and subjective response.

Misc papers on Computational Acoustics

Uncertainties of room acoustical measurements by I Witew and M Vorländer

Ali Qapu—Historical Persian music room by H Azad

Diffusion in concert halls analysed as a function of time during the decay process. By C L Christensen and JH Rindel (Presentation)

Schroeder Frequency Revisited (Forum Acusticum 2011 presentation) by M Skålevik

Room acoustical parameters at listeners’ ears—can preferred concert hall acoustics be explained? by M Skålevik

Prediction tools in acoustics—can we trust the PC? by M Vorländer

Reverberation Time—the mother of all room acoustical parameters by M Skålevik (presentation)

“The Early History of Ray Tracing in Room Acoustics” (external link) , by Peter Svensson

Diffusivity and its effect on concert hall seat absorption. (Full paper version), by M Skålevik

How dry do the recordings for auralization need to be? by A Buen

An improved low frequency radiation model for finite sound reflectors by Rathsam et.al