Sound transmission underwater -- looking for equations TX --> Rx

[paulmdrdo]

Hello! I have a system depicted below. I need to know what is the working equation that governs the transmit and receive power of the transmitter and receiver in the diagram. The transmitted signal is a sound wave and not an RF signal, the transmission is underwater. I would like to know what is the governing equation that models the transmit and receive power that also related to the distance between the tx and rx. Thank You!

 

[davenn]

The transmitted signal is a sound wave and not an RF signal, the transmission is underwater.

but the principles are the same

I would like to know what is the governing equation that models the transmit and receive power that also related to the distance between the tx and rx. Thank You!

so you will have a known TX power. What things do you think will affect the amount of power detected by the receiver ?

You have labelled you thread with an I tag ... so time for you to put a little thought into it, and people here will guide you

Dave

 

[lewando]

Too many questions for @paulmdrdo. Will you indeed have a known TX power? Or are you looking for a model of that as well? Are these commercial transducers, intended for underwater application, or are they your own design? Will you be operating in a bathtub, koi pond or the Straits of Florida? Or maybe a water-filled tube? Please provide more application details.

 

[paulmdrdo]

Hello!
@lewando
I will have a known tx power that is based on the power rating of my transducer. It's not a commercial transducer, it's home-made. here's the link for the piezoceramic ring i will be using https://www.steminc.com/pzt/en/piezo-ceramic-cylinder-26x22x13mm-43-khz. I will be testing it first in an inflatable pool. Then if my goal is achieved, I would do some adjustments to test it in the sea. I would like the necessary equations for my documentation.
I've an article that computes for the sound intensity that relates distance to the power. I = P/4pir^2. but this formula is in air not in water.
Regards,
Paul

 

[lewando]

I've an article that computes for the sound intensity that relates distance to the power. I = P/4pir^2. but this formula is in air not in water.

That equation is for a spherical spreading propagation condition. If you want to use that condition (no surfaces to constrain or interact with the propagation) but use water (or seawater) as the medium, you have to consider absorptive losses. According to this reference Principles of Underwater Sound for Engineers, Robert J Urick these losses are a function of temperature, depth, salinity, and frequency. The author provides a working equation for transmission loss for spherical spreading with absorption:
TL = 20 log r + α r 10^-3

where the absorption coefficient, α, is:
α = 0.1f²/(1 + f²) + 40f²/(4100 + f²)

(for conditions of: saltwater, zero depth, and 40 °F)

Units:
TL-- dB
r-- yards
α-- dB/kiloyard
f-- kHz

For r < 100 yards, the spherical spreading term (20 log r) is dominant, same as air, essentially.

 

[paulmdrdo]

@lewando Thank you!

Now, that we know TL. How do I relate power rating of my transmitter circuit to how far it can transmit sound wave in water?
For example, I have a 40W tx power. What is the formula should I use to calculate for the transmit distance?

also does zero depth means the source is not underwater?

 

[olivermsun]

@lewando
also does zero depth means the source is not underwater?

I believe that means you are at surface pressure.

 

[berkeman]

here's the link for the piezoceramic ring i will be using https://www.steminc.com/pzt/en/piezo-ceramic-cylinder-26x22x13mm-43-khz.

The datasheet says that cylinder is meant to be used in Hoop Mode vibration. Is that what you are wanting to use? That would not seem to be an efficient way to couple ultrasonic energy to water, unless I'm missing something. Also notice how it says that the input impedance is around 10 Ohms at resonance (in air). What do you think the input impedance is in water? Do you think it will couple well to water? I'm guessing you should find a plate US coupler that is impedance matched to the water, if you want to have an efficient system...

I have a 40W tx power.

That is a lot of power to be putting into the water. What safety considerations have you considered? Do you know of any regulations for US power levels that can be transmitted in open water by civilians?

https://www.americanpiezo.com/images/figures/table1-82.png

 

[berkeman]

That is a lot of power to be putting into the water. What safety considerations have you considered? Do you know of any regulations for US power levels that can be transmitted in open water by civilians?

Hmm, maybe that power level is okay...?

https://www.westmarine.com/WestAdvisor/Selecting-a-Fishfinder

How much transmit power, and what frequencies?
How many watts?
The power of a fishfinder—the strength of the “ping”—is expressed in watts RMS (root mean squared). Power is directly related to how well you see in silt-laden water, view down to greater depths, and successfully resolve separate targets and bottom structure. A 500-watt (RMS) fishfinder should have plenty of power for most coastal applications. Serious bluewater anglers should look for 1,000 watts or more. Inland lake fishermen can see the shallow bottom with only 200 watts.

StructureScan 3D transom mount transducer.

Frequency of the transducer(s)
Fishfinders operate using a single frequency transducer, dual frequencies, multiple frequencies or a broadband CHIRP system. See our online Advisor, Selecting a Sonar Transducer, for more about transducers. In general, higher frequencies give the finest detail resolution, the least background noise on your screen and the best view from a fast-moving boat, but don’t penetrate as deeply as lower frequencies. Shallow-water inland anglers generally choose higher frequencies of 200kHz, 400kHz or 800kHz. For maximum depth, use lower frequencies. We recommend 200kHz or higher (up to 800kHz) for water depths up to 200' and 80kHz or 50kHz for deeper waters.

 

[paulmdrdo]

The datasheet says that cylinder is meant to be used in Hoop Mode vibration. Is that what you are wanting to use? That would not seem to be an efficient way to couple ultrasonic energy to water, unless I'm missing something. Also notice how it says that the input impedance is around 10 Ohms at resonance (in air). What do you think the input impedance is in water? Do you think it will couple well to water? I'm guessing you should find a plate US coupler that is impedance matched to the water, if you want to have an efficient system...
View attachment 222543

Hello! I will use potting compound to encapsulate the transducer to prevent contact to any conductive fluid. The potting compound is Urethane which has a density identical to to that of water, providing for mechanical to acoustical energy coupling.

 

[sophiecentaur]

For example, I have a 40W tx power. What is the formula should I use to calculate for the transmit distance?

Is the "40W" figure more than a nominal figure from the spec of the amplifier that's used? The matching between the amplifier and the tansducer (and the water) can make a massive difference to the radiated power. You are in precisely the same situation as a Radio Transmitter and Antenna designer so I could suggest some reading around in that direction; there is loads more available than for ultrasound systems.. In order to know what power is being supplied to the transducer, you have to measure it in some way. You have built the unit yourself so can I presume you have some test equipment?
If you don't have much test gear then why not do some practical tests? I assume you have a receiving setup so measure the volts you get out of that at various distances. You can get away without knowing too many details by doing it that way. All that's really necessary for the communications link to work is that the signal to noise ratio is high enough. Your receive transducer can also allow you to tweak the transmitter matching for max and give you a measure of the directivity of the transmit (and receive) transducers.

 

[lewando]

What is the formula should I use to calculate for the transmit distance?

Embedded in the datasheet for the cylinder is a link to the UCSD Modem which uses that cylinder. It is informative. It includes a reference to the "passive sonar equation" (for a receiver with no directivity) which can be used to determine range:

Signal to Noise Ratio = (Source Level) - (Transmission Loss) - (Noise Level)

The Transmission Loss term has the distance embedded in it per post #5.

 

[sophiecentaur]

Hmm, maybe that power level is okay...?

From the west marine extract: " A 500-watt (RMS) fishfinder should have plenty of power for most coastal applications"
I can't believe the 500W (RMS) figure is really what they mean. How long would a 12V system stand a drain of 41A? Perhaps there's some convention that refers to RMS over the period of the 'pulse'. My depth finder would go all day when sailing without the battery suffering noticeably. I guess that no one would believe that a real 5W (or whatever) could possibly do the job.
I reckon the poor OP will have a much harder job with an Ultrasound project than he would if he were using Radio. But sometimes there's no option.

 

[lewando]

500 W is probably a pulsed rating—as in ping the fish, listen for echo. Continuous mode would probably only tenderize the fish ;)

 

[sophiecentaur]

Flying fish or frying fish?

 

[berkeman]

Embedded in the datasheet for the cylinder is a link to the UCSD Modem which uses that cylinder. It is informative. It includes a reference to the "passive sonar equation" (for a receiver with no directivity)

That is part of what confuses me about the OP and his first post. He seems to clearly show a directed channel Tx --> Rx, and then he suggests he's using a Hoop Mode omnidirectional piezo transducer.

 

[olivermsun]

That is part of what confuses me about the OP and his first post. He seems to clearly show a directed channel Tx --> Rx, and then he suggests he's using a Hoop Mode omnidirectional piezo transducer.

I'm not sure what you find so strange about it. He seems to be proposing to use an underwater transmitter-receiver pair. Especially if the transmitter and receiver are not held in some fixed geometry, one of the easiest things to do would be dangle both in the water at some reasonable (perhaps even the same) depths and transmit/receive omnidirectionally. A hoop-pattern transmitter is pretty standard for this.

 

[lewando]

How do I relate power rating of my transmitter circuit to how far it can transmit sound wave in water?

If you were to instead ask: "What is the maximum achievable (without being permanently damaged) sound pressure level of my transmitter?" you could then use the passive sonar equation to get "how far".

I have to assume you are trying to reproduce what was done with the UCSD modem. Please confirm this, or elaborate on your deviations from that reference design.

That team invested some time and effort to characterize the devices, resulting in those TVR and RVR response curves. Depending on what type and how much urethane potting compound you choose to apply to the device, you will get somewhat different results. But if you are following that reference design, use their results as a starting point. Feel free to more precisely characterize your devices if you have the resources.

 

[berkeman]

I'm not sure what you find so strange about it. He seems to be proposing to use an underwater transmitter-receiver pair. Especially if the transmitter and receiver are not held in some fixed geometry, one of the easiest things to do would be dangle both in the water at some reasonable (perhaps even the same) depths and transmit/receive omnidirectionally. A hoop-pattern transmitter is pretty standard for this.

Hello! I have a system depicted below. I need to know what is the working equation that governs the transmit and receive power of the transmitter and receiver in the diagram. The transmitted signal is a sound wave and not an RF signal, the transmission is underwater. I would like to know what is the governing equation that models the transmit and receive power that also related to the distance between the tx and rx. Thank You!

View attachment 222462

Yes, you may be right. For some reason I remembered horn antennas shown on the diagram in his OP. I see now that they are just squares, maybe implying omni transducers.