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Loudness

Most people i...

Question

Most people interpret a 9.0 dB increase in sound intensity level as a doubling in loudness. By what factor must the sound intensity be increased to double the loudness ?

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Solution

$S L = 10 l o g_{10} (\frac{I}{I_{0}})$
here, $9 = 10 l o g_{10} (\frac{2 I}{I_{0}})$
or $l o g_{10} (\frac{2 I}{I_{0}}) = 0.9$
$∴ \frac{2 I}{I_{0}} = 10^{0.9} = 7.9 \approx 8$

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