What does a measurement of 20 dB represent in terms of intensity?

When measuring sound intensity in decibels (dB), the logarithmic scale is used to express ratios of power or intensity. A change of 10 dB corresponds to a tenfold (10x) increase in intensity. Thus, if we move to a change of 20 dB, we need to consider it in terms of the base 10 logarithmic scale.

To calculate the intensity increase represented by 20 dB, we use the formula that describes the relationship between decibels and intensity:

[ \text{dB} = 10 \log_{10} \left( \frac{I}{I_0} \right) ]

where ( I ) is the intensity level, and ( I_0 ) is the reference intensity level.

If we set the difference to 20 dB and solve for the intensity ratio, we get:

[ 20 = 10 \log_{10} \left( \frac{I}{I_0} \right) ] [ 2 = \log_{10} \left( \frac{I}{I_0} \right) ] [ 10^2 = \frac{I}{I_0} ] [