<p>Ocean waves are, as the animation shows, characterized be varying amount of water over ground, or any point below surface. Therefore, they generate variable pressure on this point generating, inter alia, seismic waves that can be sensed of 100ths of KM. In fact, the seismograph I happen to have installed in my basement close to the coast, records easily heavy sea. Keyword: Microseism</p>
<p>In theory, this pressure variation is equivalent to pressure variations resulting from sound waves.</p>
<p>The frequency of this pressure variation is in the order of 1/6 s, so very infrasonic.</p>
<p>Concerning the equivalent sound pressure of this water waves, let us assume 1 m peak to peak (crest to through) corresponding to a (in-water) pressure difference of 0.1 ATM or 10 kPa or 200 dB//1uPa.</p>
<p>The loudest sound of a whale is a sperm whale click with up to 230 dB//uPa-1m. The sound of snapping shrimps is 190 dB//uPa-1m.</p>
<p>While comparable with loudest sound in animal kingdom, a major difference between these sounds is the frequencies of the pressure waves: 1/6 Hz for water-wave based, some kHz for snapping shrimps, and about 15 kHz for sperm whales. Also, water-wave base pressure waves are of long durations transforming huge amount of wind energy, while animal sound are of limited energy and therefore short in duration. Whale and dolphin pulses are typically less than 1 ms.</p>
<p>Baleen whale calls and dolphin whistles are longer, but AFAIK have lower pressure levels.</p>

CC BY-SA 4.0
2022-09-27T16:07:36.110Z
2022-09-27T17:59:03.830Z
2022-09-27T17:59:03.830Z
WMXZ
<p>In the following, I'm assuming you refer to the pressure fluctuations resulting from the change in hydrostatic pressure caused by the waves. Also, my understanding is that the pressure under a wave crest is increased in relation to the corresponding depth increase.</p>
<p>The first thing to notice is that the frequency of the &quot;signal&quot; is very low (0.1-10 Hz):
<a href="https://i.sstatic.net/hSY9L.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/hSY9L.png" alt="By Walter H. Munk - https://apps.dtic.mil/dtic/tr/fulltext/u2/a062594.pdf, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=18102158" /></a></p>
<p>This means that most animals are not capable of hearing that pressure fluctuation (some large whales might be able to hear down to 10 Hz, but not much below), and consequently, it just becomes part of the ambient pressure (their ears effectively acts as a high-pass filter, filtering out the very low frequencies).</p>
<p>But apart from not being able to hear the pressure changes, there's nothing (as far as I know) that prohibits them from sensing the pressure fluctuations in theory, and these could be sizable e.g:</p>
<p>For a receiver at 10 m depth the ambient pressure is ~G x rho_water x depth+1_atmosphere = 9.81 m/s/s x 1026 kg/m³ x 10 m + 101300 Pa = 201951 Pa ≈ 2 atm (although the ambient pressure is strictly irrelevant to the &quot;acoustic pressure&quot;).</p>
<p>Here &quot;acoustic pressure&quot; is understood as pressure deviation from short-term mean ambient pressure measured in Pa.</p>
<p>For a wave of the peak-trough height of 5 m the peak &quot;acoustic pressure&quot; is 9.81 m/s/s x 1026 kg/m³ x 2.5 m = 25163 Pa or Lpeak of 208 dB re 1 µPa² and &quot;RMS&quot; of 205 dB re 1 µPa² (I write &quot;RMS&quot; as this is just SPL over the duration of the signal)</p>
<p>I don't think this is true for the whole water column as the pressure changes probably are dissipated with depth to a certain degree, but other than this caveat there is no reason why a hydrophone should not be able to pick this up see:<a href="https://www.bksv.com/en/transducers/acoustic/microphones/hydrophones#hydrophone-specifications" rel="nofollow noreferrer">https://www.bksv.com/en/transducers/acoustic/microphones/hydrophones#hydrophone-specifications</a> (hydrophones are sensitive to very low frequencies).</p>

CC BY-SA 4.0
2022-09-27T17:03:25.767Z
as you write "acoustic pressure", you should not use (IMO) the Pa squared, right?
WMXZ
CC BY-SA 4.0
2022-09-28T07:33:17.520Z
afaik the SPL is calculated as SPL=10xLog10(Pa²/1µPa²), hence the 1µPa² reference.
I know that previously we (the acoustic community) have used SPL = 20xlog10(Pa/1µPa).
I have chosen to switch to the ISO specified definition as I makes it easy to specify my definitions and is more consistent with the original definition of a *deci*-bell.
The "20" in dB=20xLog10(Pa/1µPa) is simple a result of a simplification of the "original" decibell definition of dB=10xLog10(Pa²/Pa_ref²) (the power of 2 can be moved out of the Log function)
Rasmus
CC BY-SA 4.0
2022-09-28T10:57:39.997Z
*"I'm assuming you refer to the pressure fluctuations resulting from the change in hydrostatic pressure caused by the waves. Also, my understanding is that the pressure under a wave crest is increased in relation to the corresponding depth increase."* That's interesting; actually I was more thinking about the slow compression wave due to the movement of particles rather than the oscillatory hydrostatic pressure due to the height variation of the water column above the measurement point.
Noil
CC BY-SA 4.0
2022-09-28T10:57:45.773Z
If you look at the animation, you can see that the particle is most compressed in the longitudinal dimension when the particle is located at the upper wave crest and most compressed in the transversal dimension when the particle is located at the wave lower crest. But as pressure is not a vectorial quantity (ie does not depend on a given dimension), I'm not sure if my description makes much sense and then if this "compression" can be related to a (slow) compressionnal pressure wave. What do you think?
Noil
CC BY-SA 4.0
2022-09-28T11:45:41.213Z
I think that I don't know enough about the system to definitively give you an answer. But I interpret the animations as pressure being proportional to the density of "particles" irrespective of the direction of compression (as you write). I can however imaging that the pressure under a wave is less than if the same depth had been in still water as I think the vertical motion affects the pressure, so that the pressure fluctuations are out of phase with the wave height oscillations. We'll have to get a physicist on the case!
Rasmus
CC BY-SA 4.0
2022-09-28T14:48:31.027Z
replying to @Rasmus: I agree with you on 'deci'Bel (IIRC, I wrote it earlier on other Q). But in your answer, you wrote:  ""the peak "acoustic pressure" is "", this gives the impression that Pa² is a measure of Pressure. Also, the P in SPL stands for pressure, AFAIK. If you change "acoustic pressure" to "acoustic intensity", then there is no misunderstanding. Anyhow, the dB values are the same.
WMXZ
CC BY-SA 4.0
2022-09-27T15:35:28.617Z
2022-09-28T07:28:02.990Z
2022-09-28T07:28:02.990Z
Rasmus
<p>Ideal water waves are surface mechanical waves which are ruled by wind (disturbing force) and gravity (restoring force):</p>
<p><a href="https://i.sstatic.net/vVlAj.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vVlAj.gif" alt="enter image description here" /></a></p>
<blockquote>
<p>CC BY-NC-ND This work by Dan Russell is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at <a href="http://www.acs.psu.edu/drussell/demos.html" rel="nofollow noreferrer">http://www.acs.psu.edu/drussell/demos.html</a>.</p>
</blockquote>
<p>The motion of water particles is expected to produce a slow-oscillatory pressure wave close to the surface. As the associated water wave propagates far slower than sound waves (~m/s versus ~km/s), I believe that the pressure produced by the water wave can be approximated as an RMS pressure offset at the temporal scale of a sound wave period or as a slow RMS pressure oscillation as compared to the duration of an animal call.</p>
<p><strong>Question</strong>:</p>
<p>What is the order of magnitude of this water wave pressure offset as compared to the RMS pressure due to underwater animal communication? This question depends of several parameters, so feel free to fix some of them, e.g. water depth where water wave pressure is considered (e.g. 2m), a typical sound level of a given animal.</p>
<p>I'm just curious to know whether this slow pressure oscillation is present in practice in your underwater pressure recordings close to the surface, or if it is just negligible (I have no experience in underwater recordings), and then to better understand the relationship between acoustic waves and others types of mechanical waves as discussed in <a href="https://bioacoustics.stackexchange.com/q/950/73">this other question</a>.</p>
<p><strong>Notes:</strong></p>
<ul>
<li>I don't want to discuss any sounds that could be produced indirectly by the water wave (as in <a href="https://bioacoustics.stackexchange.com/q/521/73">this question</a>). Here, let's assume a <em>pure</em> water wave propagating slowly (~m/s) which does not produce acoustic effects (i.e. not producing any pressure wave propagating at ~km/s).</li>
<li>The type of wave I want to consider is a <em>wind wave</em> according to <a href="https://en.wikipedia.org/wiki/Wind_wave#Spectrum" rel="nofollow noreferrer">this Wikipedia entry</a> about types of water waves based on spectrum,  and maybe more precisely an <a href="https://en.wikipedia.org/wiki/Swell_(ocean)" rel="nofollow noreferrer"><em>ocean swells</em></a> according to <a href="https://en.wikipedia.org/wiki/Wind_wave#Types" rel="nofollow noreferrer">this way</a> of categorizing wind waves even if water particles move a little differently than with ideal water waves (i.e. additional drift - see <a href="https://www.acs.psu.edu/drussell/Demos/waves/Water-2016.gif" rel="nofollow noreferrer">this animation</a> versus <a href="https://en.wikipedia.org/wiki/Swell_(ocean)#/media/File:Deep_water_wave.gif" rel="nofollow noreferrer">that one</a>).</li>
</ul>

CC BY-SA 4.0
2022-09-28T08:06:15.623Z
Note that wikipedia page on wind waves has an animation that does not agree with the one you posted: https://upload.wikimedia.org/wikipedia/commons/4/4a/Deep_water_wave.gif
I don't know which is correct.
Rasmus
CC BY-SA 4.0
2022-09-28T08:35:24.250Z
yes, this is what i discussed in the 2nd bullet point of the "Note" at the end of my post.
Noil
CC BY-SA 4.0
2022-09-28T10:09:45.880Z
Good point, should've clicked those links!
Rasmus
<water><pressure><spl><background-noise><mechanics>
What is the order of magnitude of water-wave pressure as compared to that of a typical animal communication sound?
# What is the order of magnitude of water-wave pressure as compared to that of a typical animal communication sound?

(Asked by: username_0 on 2022-09-27)

Ideal water waves are surface mechanical waves which are ruled by wind (disturbing force) and gravity (restoring force):

[![enter image description here](https://i.sstatic.net/vVlAj.gif)](https://i.sstatic.net/vVlAj.gif)

> CC BY-NC-ND This work by Dan Russell is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at <http://www.acs.psu.edu/drussell/demos.html>.

The motion of water particles is expected to produce a slow-oscillatory pressure wave close to the surface. As the associated water wave propagates far slower than sound waves (~m/s versus ~km/s), I believe that the pressure produced by the water wave can be approximated as an RMS pressure offset at the temporal scale of a sound wave period or as a slow RMS pressure oscillation as compared to the duration of an animal call.

**Question**:

What is the order of magnitude of this water wave pressure offset as compared to the RMS pressure due to underwater animal communication? This question depends of several parameters, so feel free to fix some of them, e.g. water depth where water wave pressure is considered (e.g. 2m), a typical sound level of a given animal.

I'm just curious to know whether this slow pressure oscillation is present in practice in your underwater pressure recordings close to the surface, or if it is just negligible (I have no experience in underwater recordings), and then to better understand the relationship between acoustic waves and others types of mechanical waves as discussed in [this other question](https://bioacoustics.stackexchange.com/q/950/73).

**Notes:**

* I don't want to discuss any sounds that could be produced indirectly by the water wave (as in [this question](https://bioacoustics.stackexchange.com/q/521/73)). Here, let's assume a *pure* water wave propagating slowly (~m/s) which does not produce acoustic effects (i.e. not producing any pressure wave propagating at ~km/s).
* The type of wave I want to consider is a *wind wave* according to [this Wikipedia entry](https://en.wikipedia.org/wiki/Wind_wave#Spectrum) about types of water waves based on spectrum, and maybe more precisely an [*ocean swells*](https://en.wikipedia.org/wiki/Swell_(ocean)) according to [this way](https://en.wikipedia.org/wiki/Wind_wave#Types) of categorizing wind waves even if water particles move a little differently than with ideal water waves (i.e. additional drift - see [this animation](https://www.acs.psu.edu/drussell/Demos/waves/Water-2016.gif) versus [that one](https://en.wikipedia.org/wiki/Swell_(ocean)#/media/File:Deep_water_wave.gif)).

**Tags:** water, pressure, spl, background-noise, mechanics

> **Comments:**
> **username_1**: Note that wikipedia page on wind waves has an animation that does not agree with the one you posted: https://upload.wikimedia.org/wikipedia/commons/4/4a/Deep_water_wave.gif I don't know which is correct.  
> **username_0**: yes, this is what i discussed in the 2nd bullet point of the "Note" at the end of my post.  
> **username_1**: Good point, should've clicked those links!  

---

## 2 answers

### Answer by username_2 on 2022-09-27. Score: 3

Ocean waves are, as the animation shows, characterized be varying amount of water over ground, or any point below surface. Therefore, they generate variable pressure on this point generating, inter alia, seismic waves that can be sensed of 100ths of KM. In fact, the seismograph I happen to have installed in my basement close to the coast, records easily heavy sea. Keyword: Microseism

In theory, this pressure variation is equivalent to pressure variations resulting from sound waves.

The frequency of this pressure variation is in the order of 1/6 s, so very infrasonic.

Concerning the equivalent sound pressure of this water waves, let us assume 1 m peak to peak (crest to through) corresponding to a (in-water) pressure difference of 0.1 ATM or 10 kPa or 200 dB//1uPa.

The loudest sound of a whale is a sperm whale click with up to 230 dB//uPa-1m. The sound of snapping shrimps is 190 dB//uPa-1m.

While comparable with loudest sound in animal kingdom, a major difference between these sounds is the frequencies of the pressure waves: 1/6 Hz for water-wave based, some kHz for snapping shrimps, and about 15 kHz for sperm whales. Also, water-wave base pressure waves are of long durations transforming huge amount of wind energy, while animal sound are of limited energy and therefore short in duration. Whale and dolphin pulses are typically less than 1 ms.

Baleen whale calls and dolphin whistles are longer, but AFAIK have lower pressure levels.


---

### Answer by username_1 on 2022-09-27. Score: 2

In the following, I'm assuming you refer to the pressure fluctuations resulting from the change in hydrostatic pressure caused by the waves. Also, my understanding is that the pressure under a wave crest is increased in relation to the corresponding depth increase.

The first thing to notice is that the frequency of the "signal" is very low (0.1-10 Hz):
[![By Walter H. Munk - https://apps.dtic.mil/dtic/tr/fulltext/u2/a062594.pdf, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=18102158](https://i.sstatic.net/hSY9L.png)](https://i.sstatic.net/hSY9L.png)

This means that most animals are not capable of hearing that pressure fluctuation (some large whales might be able to hear down to 10 Hz, but not much below), and consequently, it just becomes part of the ambient pressure (their ears effectively acts as a high-pass filter, filtering out the very low frequencies).

But apart from not being able to hear the pressure changes, there's nothing (as far as I know) that prohibits them from sensing the pressure fluctuations in theory, and these could be sizable e.g:

For a receiver at 10 m depth the ambient pressure is ~G x rho\_water x depth+1\_atmosphere = 9.81 m/s/s x 1026 kg/m³ x 10 m + 101300 Pa = 201951 Pa ≈ 2 atm (although the ambient pressure is strictly irrelevant to the "acoustic pressure").

Here "acoustic pressure" is understood as pressure deviation from short-term mean ambient pressure measured in Pa.

For a wave of the peak-trough height of 5 m the peak "acoustic pressure" is 9.81 m/s/s x 1026 kg/m³ x 2.5 m = 25163 Pa or Lpeak of 208 dB re 1 µPa² and "RMS" of 205 dB re 1 µPa² (I write "RMS" as this is just SPL over the duration of the signal)

I don't think this is true for the whole water column as the pressure changes probably are dissipated with depth to a certain degree, but other than this caveat there is no reason why a hydrophone should not be able to pick this up see:<https://www.bksv.com/en/transducers/acoustic/microphones/hydrophones#hydrophone-specifications> (hydrophones are sensitive to very low frequencies).

> **Comments:**
> **username_2**: as you write "acoustic pressure", you should not use (IMO) the Pa squared, right?  
> **username_1**: afaik the SPL is calculated as SPL=10xLog10(Pa²/1µPa²), hence the 1µPa² reference. I know that previously we (the acoustic community) have used SPL = 20xlog10(Pa/1µPa). I have chosen to switch to the ISO specified definition as I makes it easy to specify my definitions and is more consistent with the original definition of a *deci*-bell. The "20" in dB=20xLog10(Pa/1µPa) is simple a result of a simplification of the "original" decibell definition of dB=10xLog10(Pa²/Pa_ref²) (the power of 2 can be moved out of the Log function)  
> **username_0**: *"I'm assuming you refer to the pressure fluctuations resulting from the change in hydrostatic pressure caused by the waves. Also, my understanding is that the pressure under a wave crest is increased in relation to the corresponding depth increase."* That's interesting; actually I was more thinking about the slow compression wave due to the movement of particles rather than the oscillatory hydrostatic pressure due to the height variation of the water column above the measurement point.  
> **username_0**: If you look at the animation, you can see that the particle is most compressed in the longitudinal dimension when the particle is located at the upper wave crest and most compressed in the transversal dimension when the particle is located at the wave lower crest. But as pressure is not a vectorial quantity (ie does not depend on a given dimension), I'm not sure if my description makes much sense and then if this "compression" can be related to a (slow) compressionnal pressure wave. What do you think?  
> **username_1**: I think that I don't know enough about the system to definitively give you an answer. But I interpret the animations as pressure being proportional to the density of "particles" irrespective of the direction of compression (as you write). I can however imaging that the pressure under a wave is less than if the same depth had been in still water as I think the vertical motion affects the pressure, so that the pressure fluctuations are out of phase with the wave height oscillations. We'll have to get a physicist on the case!  
> **username_2**: replying to @username_1: I agree with you on 'deci'Bel (IIRC, I wrote it earlier on other Q). But in your answer, you wrote:  ""the peak "acoustic pressure" is "", this gives the impression that Pa² is a measure of Pressure. Also, the P in SPL stands for pressure, AFAIK. If you change "acoustic pressure" to "acoustic intensity", then there is no misunderstanding. Anyhow, the dB values are the same.  

---

