# noise level (units confusion)

i had a question in one of my classes regarding SNR in underwater acoustic channels. There are a couple of terms with the unit `dB re uPa`. I know it stands for dB with reference to uPa but I am not exactly sure what it means. Can I convert it to dB. If yes, how?

Thanks in advance!!

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## 1 Answer

dB$\mu$Pa would mean "dB's with respect to 1 $\mu$Pa".

If I have a pressure of X Pascals, then to express it in dB$\mu$Pa, I would compute

$$20log_{10}(\frac{X}{1\mu Pa})$$

i.e

$$20log_{10}(10^6X)$$

since there are $10^6$ $\mu$Pa per Pa.

So the rule is: compute how many micropascals you have and take $20log_{10}$ of that number.

For the second part of your question, "converting it to dB", you would have to specify exactly which dB quantity you were interested in. Wikipedia lists a rather large number of options.

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2
The general rule about finding dB is a little more complicated than this suggests. dBmW is "dB's with respect to 1 milliwatt." If we have a power M mW, in dB we have: $10 log_{10}(M/1 mW)$. We use a factor of 20 for units we have decided are Amplitude and a factor of 10 for units we have decided are Intensity. The general idea is 10 X as much energy is 10 dB higher, energy $\propto$ Ampitude$^2$. – mwengler Apr 29 '12 at 17:12
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