If the amplitude of a sound wave is tripled,
By how many $d B$ will the sound level increase?

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Solution

An increase in amplitude of sound by a factor of two corresponds to 6.02 dB
from a relation that,

$20 l o g_{(} 10) \frac{a}{a_{o}}$

New amplitude will be, $a = 3 a_{o}$

$20 l o g_{(} 10) \frac{3 a}{a}$

$20 \times 0.477$

$= 9.54$

So, 9.54 times db will sound level increase.

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