Sound in decibels is measured by comparing the sound intensity, I, to a benchmark sound I0 with intensity 10-16 watts/cm2. Then,

Question

Noise level in decibels      = 10⁢  log⁢  (II0).

Sound A measures 31 decibels and sound B is 8 times as loud as sound A. What is the decibel rating of sound B to the nearest integer?

Answer 1

Your equation for decibel level should be 10 log(I/I₀)

Any way, if you go from I1 to I2, the decibel difference dbB - dbA = 10log(IB/I0) - 10log(IA/I0) or (using the log rule that the log a - log b is log (a/b) 10log(IB/IA) = dbB - dbA.

You know IB/IA and dbA --> solve for dbB

Good luck!