Question

If a sound has an intensity of 1/10th of the intensity of a louder sound, how much smaller on the decibel scale it the loudness of the less intense sound?

Answer 1

uses a log base ten scale, so goes down by 1

Answer 2

So what would the answer be?

Answer 3

10?

Answer 4

The number of decibels is ten times the logarithm to base 10 of the ratio of the two values of intensity:
\[Logarithmic\ ratio\ (dB)=10\log_{10} 10\]

Answer 5

or put another way, since it is a log scale base ten an increase of 1 on the scale is ten times as intense, and a decrease of 1 is one tenth as intense