What is the acoustic power output of a blue whale in Watts?

[Jiggy-Ninja]

I didn't think it would be this hard to find the answer to this, but 1 hour of googling has come up with nothing that I can make sense of. The main cause of my confusion is that there's about a dozen different ways of measuring sound power in decibels with different units or reference powers, with some being based on source power and others being $\frac{W}{m^{2}}$ at some standard distance, and I can't figure out how to convert them!

The question I want answered is simple:

What is the RMS power, in Watts, of a whale song?

I was unable to find a straight answer for this no matter what queries I put in. Google seemed more interested in giving me pages about "the relaxing power of whale song", but I'm stunned at how hard it is to find a simple figure for something so basic.

I found some figures on wikipedia: http://en.wikipedia.org/wiki/Whale_vocalization

Arbitrarily, I chose the blue whale and took the high end of the range, 188 dB. The trouble is the units, listed at the top of the table, are "dB re 1 uPa (micropascal) at 1m (meter)".

So, this dB ratio is based on pascals at a specified distance. I want to convert this into straight power in watts, and do not know how. Can anyone help? Or even just point a link to some place with a simple answer.

 

[Bobbywhy]

You may be able to find your answer here:

http://www.sengpielaudio.com/calculator-soundlevel.htm

 

[Jiggy-Ninja]

Saw that. Problem is that the reference pressure level is 20 micropascals, which I understand is the standard for air measurements because it is considered the faintest sound a human can hear. The 188 dB level from wikipedia is based on 1 micropascal @ 1 meter, a different reference pressure.

 

[Jiggy-Ninja]

Does anyone know an answer to this?

 

[Bobbywhy]

The book, “The Sonar of Dolphins”, Page 129 describes how acoustic power in watts/m2 radiated by an omnidirectional source is calculated. Then the radiated power of a directional source (using the directivity index) is calculated. Finally, the radiated power from a directional source can be expressed in Watts using equation (7-11). That radiated power should be evaluated at a distance of 1 m from the source.

Page 130, Figure 7.15 shows a graph of peak-to-peak source level (dB re 1 microPascal) versus Acoustic power in Watts. The largest amplitude dolphin click measured while obtaining the data in the graph was 230 dB, which represents 59 Watts of acoustic power.
See:
http://books.google.com/books?id=Q3...epage&q=sonar acoustic power in watts&f=false

 

[Jiggy-Ninja]

Looks like the kind of thing I was looking for. Let me see if my calculations are right.

Starting with the 188 dB level I got, solving the following equation:
$$188 dB = 20\times log\left( \frac{P}{1μPa} \right)$$
I get P = 2.51 kPa @ 1 m for RMS wave pressure of the song.

Using formula 7-8 in the book you linked, I calculate the intensity to be 3.97 W/m² @ 1 m. Using equation 7-9, the source power of the song comes up to be about 50 Watts. Does this sound reasonable for a whale? I don't have much experience with sound, especially underwater, so I don't know what a good ballpark might be for this kind of thing.

 

[Bobbywhy]

Your result of ~50 Watts of "source power" for the blue whale's 188 dB seems correct considering the largest amplitude dolphin click measured while obtaining the data in the graph was 230 dB, which represented 59 Watts of acoustic power. The term you used "source power" is not common in sonar work. You may benefit from studying the Active and Passive Sonar equations. Normally they refer to "Source Level" and the units are (as you've seen) dB re 1 micropascal.

No one I know in underwater acoustics uses watts for measuring acoustic power. I cannot figure out why you want to.

 

[Jiggy-Ninja]

Your result of ~50 Watts of "source power" for the blue whale's 188 dB seems correct considering the largest amplitude dolphin click measured while obtaining the data in the graph was 230 dB, which represented 59 Watts of acoustic power. The term you used "source power" is not common in sonar work. You may benefit from studying the Active and Passive Sonar equations. Normally they refer to "Source Level" and the units are (as you've seen) dB re 1 micropascal.

No one I know in underwater acoustics uses watts for measuring acoustic power. I cannot figure out why you want to.

I don't do underwater acoustics work either, I'm actually studying electrical engineering. I'm currently writing a paper about electronic ultrasonic communication networks, which are primarily used underwater. I was thinking of using whale song as a sort of biological example to provide some features for comparison. dB re 1 uPa is not a valid unit to compare to the power of an electronic transducer, so I needed to convert it.

Thank you for your help. I was able to get what I needed.

 

[Bobbywhy]

You’re welcome. If you had described your project in complete detail in your opening post it would have been more efficient for others to respond with more utilitarian comments. So, you are writing a paper on Ultrasonic Communication Networks! Several commercial companies offer “off the shelf” systems and, more importantly, they provide lots of technical information, including the units used in their technical specifications. You may find a plethora of information through searches for these systems.

The statements: “No one I know in underwater acoustics uses watts for measuring acoustic power. I cannot figure out why you want to.” are based on my experience of a quarter century immersed in underwater acoustic engineering.

Transducer, Part number 09233/000, the electrical driving power and the acoustic output power are characterized this way:
“The electrical power driving the piezo-ceramic transducer at 150 kHz is 600 Watts when driven up to 2% duty cycle. The output acoustic power (in water) is 155 dB re 1micropascal.”
http://www.morganelectroceramics.co...nic-transducers-for-marine-electronics-sonar/

For an excellent reference with clearly written definitions, see the below site:

“Sound levels extend over many orders of magnitude and, for this reason, it is convenient to use a logarithmic scale when measuring sound. Both Sound Pressure Level (SPL) and Sound Intensity Level (SIL) are measured in decibels (dB) and are usually expressed as ratios of a measured and a reference level:
Sound Pressure Level (dB) = 20 log (p/pref) where pref is the reference pressure
Sound Intensity Level (dB) = 10 log (I/Iref) where Iref is the reference intensity”
http://www.fas.org/man/dod-101/sys/ship/acoustics.htm#intensity