How do I measure loudness level of a device in environment?

I want to measure the individual loudness level of a device in environment.

Fistly, I measure loudness level when the device is ON (95.5dB) Then I measure loudness level when the device is OFF (48.5dB)

The engineer said that the device loudness level is 95.5-48.5=47dB

But I think it must be ~95.5 because it still depending in many factor such as: environment sound frequency and device sound frequency...

• What is your definition of "loudness level"? – ACuriousMind May 16 '17 at 11:39
• You are correct, but not for the reasons you mention. A proper dB calculator can be found here noisemeters.com/apps/db-calculator.asp – user126422 May 16 '17 at 11:42
• @ACuriousMind: sorry for the confuse. I mean "loudness level" is simple loudness measuring by dB – sonpython May 16 '17 at 11:52
• @WillyBillyWilliams you rock man!!!! – sonpython May 16 '17 at 11:54
• @sonpython Oh boy, you made me blush – user126422 May 16 '17 at 11:57

Here's the math: If $\beta$ is the level in dB and I is the intensity (power/area) in watts per square meter, $$\beta=10\log\left(\frac{I}{10^{-12}}\right).$$ Inverting that we get that $$I=10^{-12}\cdot 10^{\beta/10}.$$ $$\beta = 95.5\ \mathrm{dB} \to I = 3.548\times 10^{-3}\ \mathrm{W/m}^2$$ $$\beta = 48.5\ \mathrm{dB} \to I = 7.079\times 10^{-8}\ \mathrm{W/m}^2$$

A reasonable assumption for non-coherent sound sources is that the intensities add, so subtracting the background intensity be get the device intensity is $$I = 3.548\times 10^{-3}\ \mathrm{W/m}^2$$ which has a level of $95.5$ dB

Just talk with supporter from noisemetters, he explained:

Mike:

Hi Michael

Mike:

The loudness will be 95.5

Michael Phan:

can you confirm that the loudness of the device is 95.5

Mike:

Yes, you can't mathematically subtract decibel levels as the decibel scale is logarithmic.

Michael Phan:

thank you

Mike:

Any level that is 12dB or more above the background noise level will not be influenced by the background level

Mike:

Is there anything else I can help you with

Michael Phan:

thank you Mike

Michael Phan:

have a nice day

Mike:

You too.