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

Answer 1

The loudness of a sound is given in watts per square meter. The loudness of a sound in decibels is given as

10 x log (P_a / P_t), where P_a the ambient sound power per square meter and P_t is the power at the threshold of hearing. (10^-12 W/m²)

A 90 dB sound is then 90 db = 10 x log P₉₀ / P_t.. Taking the antilog gives P₉₀ = P_t x 10⁹ For the 170 dB sound, P₁₇₀ = P_t x 10¹⁷.

The ratio P₁₇₀ / P₉₀ = P_t x 10¹⁷ / P_t x 10⁹ = 10¹⁷ / 10⁹ = 10⁸. So, the 170 dB sound is 10⁸ louder than the 90 dB sound.

Another way of looking at it, two sounds that differ by X dB, the higher dB sound is a factor of 10^x/10 more intense that the lower dB sound.