<p>As Thejasvi's <a href="https://bioacoustics.stackexchange.com/a/338/95">answer</a> explained, decibels always express a ratio between two quantities: a measurement/value and a reference. The issue is defining what are the quantities being expressed, and this depends on application and quantity being presented. Often the reference value is left implicit; in underwater acoustics the reference acoustic pressure for Sound Pressure Level is <em>almost</em> always 1 µPa [ <span class="math-container">$=10^{-6}$</span> Pa] RMS, and in airborne acoustics is it <em>almost</em> always 20 µPa RMS. It is generally good practice to clearly state your reference at least once when presenting your work/paper: &quot;<em>all SPL values herein are presented in dB re 20 µPa</em>&quot;, or something on those lines.</p>
<p>For example, you can express a ratio of <strong>amplitudes</strong> using <span class="math-container">$20\log_{10}$</span>(amplitude/ref_amplitude). Say, a measured acoustic pressure of 1 mPa RMS compared to a reference pressure of 1 µPa RMS defines a Sound Pressure Level (SPL) of <span class="math-container">$20\log_{10}\left( \frac{10^{-3}}{10^{-6}}\right)$</span> = <strong>60 dB [re 1 µPa RMS]</strong>.</p>
<p>Alternatively, you can express a ratio of <strong>energies</strong> (or <strong>powers</strong>) using <span class="math-container">$10\log_{10}$</span>(energy_value/ref_energy_value). For example, <a href="https://en.wikipedia.org/wiki/Signal-to-noise_ratio" rel="nofollow noreferrer">signal-to-noise ratio (SNR)</a> is generally defined as the ratio between the signal energy to the noise energy, and is calculated as <span class="math-container">$10\log_{10}$</span>(signal_energy/noise_energy). Energies and powers are generally proportional to signal amplitude squared, so they are often presented in units of &quot;acoustic pressure squared&quot;. For example, a measured signal power of <span class="math-container">$10^{-6}$</span> Pa<span class="math-container">$^2$</span> (notice the units of &quot;acoustic pressure squared&quot;) relative to a noise power of <span class="math-container">$0.5 \times 10^{-6}$</span> Pa<span class="math-container">$^2$</span> defines a SNR of <span class="math-container">$10\log_{10} \left( \frac {10^{-6}}{0.5 \times 10^{-6}} \right)$</span> = <strong>3 dB</strong>. There is no fixed reference value in this case, and the important quantity here is the ratio itself, so it is generally presented as a &quot;pure&quot; ratio in dB, without an explicit reference.</p>

CC BY-SA 4.0
2022-07-06T20:00:55.363Z
I think it is important to note that dB always refer to energy. Using squared pressure as a stand in for energy uses the general linear physics principal of equipartition, i.e. the energy in the acoustic pressure and acoustic velocity are equal.
nedlrichards
CC BY-SA 4.0
2022-07-06T10:26:31.517Z
2024-02-21T02:23:45.627Z
2024-02-21T02:23:45.627Z
fabio_hirono
<p>The inconsistent absence/presence of dB references can be very confusing indeed. A dB (short for decibel) is a ratio of two values/measurements ( <span class="math-container">$20\log_{10}\frac {B}{A}$</span> or <span class="math-container">$10\log_{10}\frac {B}{A}$</span>).</p>
<p>When referring to a sound level, good practice says the reference value (<span class="math-container">$A$</span> here) should always be explicitly mentioned. If a sound level is reported as e.g. '20 dB' without further context, it's kind of like saying '<span class="math-container">$B$</span> is 10 times <span class="math-container">$A$</span>', but we don't know the actual value of <span class="math-container">$B$</span> because <span class="math-container">$A$</span> is unspecified. In case of sound levels, the actual value of the reference <span class="math-container">$A$</span> is very important - thus the need to specify reference (conventionally 1 µPa in aquatic and 20 µPa in terrestrial acoustics).</p>
<p>When referring to SNR however, the 'reference' A is actually the level of the background sound or noise. Here the actual value of the reference is not as important as the <em>relative magnitude</em> of the noise with reference to your signal of interest, and thus the reference value is not stated. Essentially, an SNR of 20 means 'My signal is 10 times stronger than my noise' - and this is sufficient to understand the data in this context.</p>

CC BY-SA 4.0
2022-07-06T08:47:41.417Z
2022-10-20T14:13:53.863Z
2022-10-20T14:13:53.863Z
Thejasvi
<p>I would add that providing reference levels is especially helpful to understand differences in levels that are measured in air versus in water. The in air reference is 20 µPa @ 1 m versus 1 µPa @ 1 m in water. In the past, there have been occasions where sound pressure levels for underwater values have been directly compared with those in air leading to misunderstanding of the overall SPL underwater. One way I have heard this explained really clearly (to me anyway) is an analogy to temperature. If your reference is Celsius, then 40 degrees is really hot. If you reference is Fahrenheit, it's quite cool. If you are from the US and I tell you it's 40 degrees out without the reference, you might end up in a parka on a beach in Brazil.</p>

CC BY-SA 4.0
2022-07-07T18:31:29.390Z
2022-10-20T14:08:37.593Z
2022-10-20T14:08:37.593Z
Kate Stafford
<p>&quot;Different formats for reporting acoustic measurements can be confusing, especially with varied abbreviations. Consistency and clarity are essential for understanding.&quot;</p>

CC BY-SA 4.0
2024-02-21T20:04:03.490Z
This does not provide an answer to the question. Once you have sufficient [reputation](https://bioacoustics.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](https://bioacoustics.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](https://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/late-answers/584)
selene
CC BY-SA 4.0
2024-02-17T07:31:07.120Z
2024-02-17T07:31:07.120Z
SEAC
<p>I've come across several different formats for reporting acoustic measurements. One that has particularly confused me is when someone reports the source level of something as, for example, &quot;<em>120 dB re 1 µPa</em>&quot;, and sometimes people seem to abbreviate this to &quot;<em>dB</em>&quot;.</p>
<p>However, there are other instances where a <strong>SNR</strong> (signal-to-noise ratio) is being described as just &quot;<em>dB</em>&quot; - is this being abbreviated too? Why do I not see reference units for the dB on an SNR measurement?</p>

<measurement><db><snr>
"dB [re 1 µPa]" notation - why sometimes with a reference, and sometimes without?
# "dB [re 1 µPa]" notation - why sometimes with a reference, and sometimes without?

(Asked by: username_0 on 2022-07-06)

I've come across several different formats for reporting acoustic measurements. One that has particularly confused me is when someone reports the source level of something as, for example, "*120 dB re 1 µPa*", and sometimes people seem to abbreviate this to "*dB*".

However, there are other instances where a **SNR** (signal-to-noise ratio) is being described as just "*dB*" - is this being abbreviated too? Why do I not see reference units for the dB on an SNR measurement?

**Tags:** measurement, db, snr


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## 4 answers

### Answer by username_1 on 2022-07-06. Score: 12

As username_3's [answer](https://bioacoustics.stackexchange.com/a/338/95) explained, decibels always express a ratio between two quantities: a measurement/value and a reference. The issue is defining what are the quantities being expressed, and this depends on application and quantity being presented. Often the reference value is left implicit; in underwater acoustics the reference acoustic pressure for Sound Pressure Level is *almost* always 1 µPa [ $=10^{-6}$ Pa] RMS, and in airborne acoustics is it *almost* always 20 µPa RMS. It is generally good practice to clearly state your reference at least once when presenting your work/paper: "*all SPL values herein are presented in dB re 20 µPa*", or something on those lines.

For example, you can express a ratio of **amplitudes** using $20\log\_{10}$(amplitude/ref\_amplitude). Say, a measured acoustic pressure of 1 mPa RMS compared to a reference pressure of 1 µPa RMS defines a Sound Pressure Level (SPL) of $20\log\_{10}\left( \frac{10^{-3}}{10^{-6}}\right)$ = **60 dB [re 1 µPa RMS]**.

Alternatively, you can express a ratio of **energies** (or **powers**) using $10\log\_{10}$(energy\_value/ref\_energy\_value). For example, [signal-to-noise ratio (SNR)](https://en.wikipedia.org/wiki/Signal-to-noise_ratio) is generally defined as the ratio between the signal energy to the noise energy, and is calculated as $10\log\_{10}$(signal\_energy/noise\_energy). Energies and powers are generally proportional to signal amplitude squared, so they are often presented in units of "acoustic pressure squared". For example, a measured signal power of $10^{-6}$ Pa$^2$ (notice the units of "acoustic pressure squared") relative to a noise power of $0.5 \times 10^{-6}$ Pa$^2$ defines a SNR of $10\log\_{10} \left( \frac {10^{-6}}{0.5 \times 10^{-6}} \right)$ = **3 dB**. There is no fixed reference value in this case, and the important quantity here is the ratio itself, so it is generally presented as a "pure" ratio in dB, without an explicit reference.

> **Comments:**
> **username_2**: I think it is important to note that dB always refer to energy. Using squared pressure as a stand in for energy uses the general linear physics principal of equipartition, i.e. the energy in the acoustic pressure and acoustic velocity are equal.  

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### Answer by username_3 on 2022-07-06. Score: 9

The inconsistent absence/presence of dB references can be very confusing indeed. A dB (short for decibel) is a ratio of two values/measurements ( $20\log\_{10}\frac {B}{A}$ or $10\log\_{10}\frac {B}{A}$).

When referring to a sound level, good practice says the reference value ($A$ here) should always be explicitly mentioned. If a sound level is reported as e.g. '20 dB' without further context, it's kind of like saying '$B$ is 10 times $A$', but we don't know the actual value of $B$ because $A$ is unspecified. In case of sound levels, the actual value of the reference $A$ is very important - thus the need to specify reference (conventionally 1 µPa in aquatic and 20 µPa in terrestrial acoustics).

When referring to SNR however, the 'reference' A is actually the level of the background sound or noise. Here the actual value of the reference is not as important as the *relative magnitude* of the noise with reference to your signal of interest, and thus the reference value is not stated. Essentially, an SNR of 20 means 'My signal is 10 times stronger than my noise' - and this is sufficient to understand the data in this context.


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### Answer by username_4 on 2022-07-07. Score: 7

I would add that providing reference levels is especially helpful to understand differences in levels that are measured in air versus in water. The in air reference is 20 µPa @ 1 m versus 1 µPa @ 1 m in water. In the past, there have been occasions where sound pressure levels for underwater values have been directly compared with those in air leading to misunderstanding of the overall SPL underwater. One way I have heard this explained really clearly (to me anyway) is an analogy to temperature. If your reference is Celsius, then 40 degrees is really hot. If you reference is Fahrenheit, it's quite cool. If you are from the US and I tell you it's 40 degrees out without the reference, you might end up in a parka on a beach in Brazil.


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### Answer by username_5 on 2024-02-17. Score: -1

"Different formats for reporting acoustic measurements can be confusing, especially with varied abbreviations. Consistency and clarity are essential for understanding."

> **Comments:**
> **username_6**: This does not provide an answer to the question. Once you have sufficient [reputation](https://bioacoustics.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](https://bioacoustics.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](https://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/late-answers/584)  

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