Sone - Formulas

Formulas

Loudness N in sones (for LN > 40 phon):

N = \left(10^{\frac{L_N-40}{10}}\right)^{0.30103} \approx 2^{\frac{L_N-40}{10}}

or loudness level LN in phons (for N > 1 sone):

L_N = 40 + \frac{10 \log_{10}(N)}{log_{10}(2)}

Corrections are needed at lower levels, near the threshold of hearing.

These formulas are for single-frequency sine waves or narrowband signals. For multi-component or broadband signals, a more elaborate loudness model is required, accounting for critical bands.

To be fully precise, a measurement in sones must be specified in terms of the optional suffix G, which means that the loudness value is calculated from frequency groups, and by one of the two suffixes D (for direct field or free field) or R (for room field or diffuse field).

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