Approximately how many times louder is a 170-dB sound than a 90-dB sound?

Answer 1

First, 1dB = 0.1B.

Therefore the two loudness level can be expressed as 17B and 9B.

Secondly, loudness measured in B is not the actual energy of the sound, but its logarithm.

And the energy level is thus the exponential of the B quantity.

That means, the two energy levels are proportional to

10¹⁷ and 10⁹.

Therefore the ratio of loudness is

10¹⁷/10⁹ = 10⁸ = 100,000,000.