Suppose that you and I are having a singing contest, and you produce a sound intensity (measured in W/ m2) about 32 times greater than mine. How many dB louder than me are you singing ?

Question

His is 30dB.
For 79 times greater the answer is 19dB
For 63 times greater the answer is 18dB

How do I calculate for 32 times greater

Answer 1

Let the two intensities be I1 and I2.

10 log(10)I2 - 10log(10)I1
= dB difference
= 10 log(10)[I2/I1]
= 10log(10)32 = 15.1 dB

It doesn't matter what sound intensity power units are used. It is the intensity ratio that matters.