Abstract
A stationary loudness model has been built up on the basis of the former ISO 226: 1987 concerning equal-loudness-level contours. The loudness and loudness level expressions derived in the study include the same parameters as used when determining the equal-loudness-level contours of the former ISO standard. However, as an additional main idea, a loudness summation rule has been proposed in the study. Moreover, the loudness expressions have been normalised to give the same values for people who have a similar sense of hearing. It has also been found that the loudness expressions include basically two different weightings. The first weighting is a conservative frequency weighting in the domain of sound pressure level, and the second weighting consists of coefficients applied to the weighted sound pressure levels. The latter have the greatest effect on the very low-frequency range. Finally, the paper includes a new way to use the A-weighting which takes into account the compressed character of the equal-loudness-level contours at the low frequency range. This method remarkably transforms the character of the A-weighting as a measure for low-frequency environmental noise.
Highlights
In [1] it was shown that an equal-loudness-level contour can be calculated according to an equation of the following type: How to cite this paper: Parmanen, J. (2014) Loudness Summation and Weightings for Loudness and Environmental Noise Assessment
A certain logarithmic base of two was used with an additive constant of 40 dB2 when determining the loudness levels, and the levels were only used for numerical assignment in the way that we use decibels for characterising the sound pressures
The logarithmic base was chosen on the basis of Stevens’ power law and gave the first final result (Equation (10)) that the derived loudness level does not need any additive constant in this respect
Summary
In [1] it was shown that an equal-loudness-level contour can be calculated according to an equation of the following type: How to cite this paper: Parmanen, J. (2014) Loudness Summation and Weightings for Loudness and Environmental Noise Assessment. In Equation (1), ki (the root notation) represents the inverse of the exponent of intensity at each frequency band which has the value of 3.3 (0.3 ≈ 1/3.3) at 1000 Hz band and takes the value shown in Table 1 at the other 1/3 octave band frequencies, and τi (in Table 1) is a frequency weighting defined in the domain of sound pressure level at each frequency band. A well-defined stationary loudness model may be necessary when developing more advanced dynamic loudness models
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