# Are W/m^2 and dB both units of sound intensity? What is the difference between them?

Mar 21, 2017

See below.

#### Explanation:

Human perception of loudness (aka sound intensity) is observed to be proportional to log of the scientifically measured intensity.

So a scientific machine will measure sound intensity as it is defined - as sound power per unit area whose units are $\frac{W a t \setminus t s}{m} ^ 2$.

But if the measurements are for human consumption, say the volume switch on a TV, it is better to use a log scale.

So, if we have measured ${I}_{o}$ as being the standard threshold of hearing intensity, ie what you can just about hear, in $\frac{W a t \setminus t s}{m} ^ 2$, we get a more user-friendly metric ${I}_{\mathrm{dB}}$ if we say that:

${I}_{\mathrm{dB}} = 10 {\log}_{10} \left(\frac{I}{{I}_{o}}\right) \ast \mathrm{de} c i b e l s \ast$

This means, for example, if $I = {I}_{o}$ then ${I}_{\mathrm{dB}} = 0$.