Pre-Calculus probl

Question

How much more intense is a sound at the level of the threshold of pain (110 dB) than a conversation at 48 dB?

A sound at the level of the threshold of pain (110 dB) is................ times as intense as a conversation at 48 dB.

Answer 1

The decibel is defined as a logarithmic unit of sound intensity log(I/I₀) = dB/10 [=] bels (I₀ = 10^-12 W/m²)

You can take the difference of two decibel readings and connect it to intensity ratio:

log(I₂/I₀)-log(I₁/I₀) = (1/10) (dB₂-dB₁)

in this case I₂/I₁ = 10^((1/10)(110-48)dB) = 1.58 x 10⁶ (note every bel is a factor of 10, so this is 6+ bels)