# 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?

-

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.

-
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
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9356060028076172, "perplexity": 392.25100847558065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645151768.51/warc/CC-MAIN-20150827031231-00040-ip-10-171-96-226.ec2.internal.warc.gz"}