Question

if the intensity is increased by a factor of 20, by how many decibles is the sound level increased ?​

Answer 1

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★ Let the initial intensity be I and the sound level be $\beta _{1}.$

when the intensity is increased to 20i the level increased to $\beta _{2}.$

$= > \beta _{1} = 10log( \frac{i}{I} )$

$= > \beta _{2} = 10log( \frac{20i}{I} )$

$= > 10log \: \: 20$

$= > 13db$

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Answer 2

Let the initial intensity be I and the sound level be \beta _{1}.β1.

when the intensity is increased to 20i the level increased to \beta _{2}.β2.

= > \beta _{1} = 10log( \frac{i}{I} )=>β1=10log(Ii)

= > \beta _{2} = 10log( \frac{20i}{I} )=>β2=10log(I20i)

= > 10log \: \: 20=>10log20

= > 13db=>13db