A comparative analysis of acoustic energy models for churches
(a) Shape of the energy decay curve obtained with model observed at different distances from the source. The early reflected energy (from to ) is given by an exponential energy decay having the same time constant of the late part but estimated at a later time (multiplied by ). (b) Shapes of the energy decay curve obtained with the linear model (---) and with the multi-rate exponential model (–––) observed at different distances from the source. Dotted curve represents classical exponential decay.
Plans of the second set of 12 churches surveyed. (a) Basilica of Santa Maria Maggiore in Rome, (b) Basilica of Saint Paul outside-the-walls in Rome, (c) Sant’Ambrogio in Milan, (d) Bari Cathedral, (e) Abbey of Chiaravalle della Colomba in Alseno, (f) Orvieto Cathedral, (g) Santa Maria della Consolazione in Todi, (h) Sant’Andrea in Mantua, (i) Sant’Agnese in Agone in Rome, (j) San Lorenzo in Turin, (k) Santa Maria del Carmelo in Bari, and (l) Padre Pio Pilgrimage church in San Giovanni Rotondo. (Same scale for all the churches.)
Plot of measured (●) and predicted values of the strength (left), clarity (center), and center time (right) index at 1 kHz vs source-receiver distance according to the three models considered, revised theory (…), model (- - -), and modified theory (—). (a) ACC, (b) SAD, (c) SGR.
rms error between measured and theoretical values of sound strength (a), clarity (b), and center time (c), at 1 kHz frequency band: theoretical values calculated with revised model, model, and modified model with the new classification. Error bars represent the standard deviation of point-to-point differences between measured and predicted values.
Plot of variations due to bad parameter estimation calculated for strength (left), clarity (center), and center time (right) index at 1 kHz as a function of source-receiver distance according to model (- - -) and modified theory (—). Thicker curves correspond to reference values calculated assuming , , , , , and . Thinner curves correspond to and . Error bars represent variations corresponding to .
Values of the mean scattering coefficient according to the chancel typology.
Basic details of the first set of churches surveyed.
Basic details of the second set of churches surveyed.
Values of the parameter in the first set of churches surveyed, and corresponding rms errors in the prediction of strength, clarity, and center time.
Classification of values according to typological style, with corresponding examples, and mean values.
Incremental values of and according to the architectural characteristics.
Summary of experimental values for each church surveyed, together with those assigned according to the old and the new classifications and absolute differences from experimental values. The variations in rms error resulting from application of the new classification, with reference to prediction of , , and , are also reported for each church.
Values of the coefficient derived for an application of the and modified models to the second set of churches. (scattering), , , scattering elements, and .
rms error between measured and predicted values of sound strength, clarity, and center time, at frequency bands from 125 Hz to 4 kHz. Predicted values calculated with revised model, modified model, and model.
rms average of the difference between errors corresponding to and values assigned in Table VIII and errors obtained when typological class is badly selected. Upper class corresponds to and , whereas lower class corresponds to and . All values refer to at 1 kHz octave band.
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