Question

If the intensity increased by a factor of 20, byhow may decibels is the sound level increased?

Answer 1

Let the initial intensity be I and te sound level be `beta_1`. When the intensity is increased to 20 I, the level increases to `beta_2`.
`Then beta_1=10log(I/I_0)`
and `beta_2=10log(20I/I)`
`Thus, beta_2-beta_1=10log(20I/I)`
`=10log 20`
`=13dB`.