# The sound level at a point is increased by 30 decibels. By what factor is the amplitude increased ?

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Jan 2, 2018

1000

#### Explanation:

The bel is defined logarithmically, meaning an increase of 1 bel indicates the amplitude increasing by a factor of 10. Since 10 decibels = 1 bel, an increase of 10 decibels indicates the amplitude increasing by a factor of 10.

Since 30 decibels is 3 lots of 10 decibels, the amplitude is increased by 3 factors of 10, or ${10}^{3} = 1000$.

In general, an increase of $n$ decibels indicates an increase in amplitude by a factor of ${10}^{\frac{n}{10}}$.

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