SNR for an underwater acoustic signal

In summary, the individual is seeking assistance with modeling the transmission loss and signal-to-noise ratio of an acoustic signal underwater. They are using a mathematical expression to model the transmitted signal and are trying to find the transmission power (P) using sound level (SL) data. After referencing the Matlab documentation, they have determined that P can be found using the intensity of the source and the reference intensity of sound in water. However, the calculated power does not seem accurate and the individual is also unsure about their calculations for the SNR. They are looking for expert help in resolving these issues.
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JAP
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TL;DR Summary
How could I find the SNR of an acoustic signal knowing its sound level (db ref uPa @1m)
Hi, I'm trying to model the transmission loss and SNR of an acoustic signal underwater. I'm using this expression to modelize the transmitted signal:
y = sqrt(P)*exp(1i*2*fr*pi*t)'​
where P is the transmission power in watts, fr is the transmission frequency and t is the acquisition time.
The only data I have to find P is the sound level (SL) of my source that is supposed to be 142 dB ref 1uPa at 1 meter from the source. According to the Matlab documentation site (https://fr.mathworks.com/help/phased/ug/sonar-equation.html) sound level can be defined as:
SL = 10log10(I/Iref)​
where I is the intensity from the source in W/m^2 and Iref is the reference intensity of sound in water which value is 6.667*10^-19 W/m^2. Knowing the SL value, I can isolate I to find the acoustic pressure p_rms and then the power P because I can be defined as follows:
I=p_rms^2/ρc and I = P/4*pi*r^2
where p_rms: signal acoustic pressure in Pascal, ρ: water density (1000kg/m^3), c: sound speed in water (1500 m/s)
Putting these two equations together, I can find P that should be :
P = p_rms^2*(4*pi*r^2)/(ρc)
However, when I use the value of my source (142 dB), I get a power of 1.33 mW! I believe it doesn't make sense 'cause the signal source should be detected at the receiver at least at 500 m from the source.
With regard to the SNR, I use the passive sonar equation, however I find very optimist results (i.e. more than 20 dB for a range of 800m...) so I'm not really sure my calculations are right. If there's any pro in the underwater acoustics field that could give me a hand to resolve this, I will be very grateful.
Thanks!

JAP
 
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Related to SNR for an underwater acoustic signal

1. What is SNR for an underwater acoustic signal?

SNR stands for Signal-to-Noise Ratio, and it is a measure of the strength of a signal compared to the background noise in a given environment. In the context of underwater acoustics, SNR refers to the ratio of the desired acoustic signal to the ambient noise in the water.

2. Why is SNR important for underwater acoustic signals?

SNR is important because it directly affects the quality and reliability of the received signal. A higher SNR means a stronger and clearer signal, while a lower SNR can result in a weaker and more distorted signal. This is especially crucial in underwater environments where noise levels can be high due to various factors such as marine life, weather conditions, and man-made activities.

3. How is SNR calculated for an underwater acoustic signal?

SNR is calculated by taking the ratio of the power of the desired signal to the power of the background noise. The power of a signal is measured in decibels (dB), and a higher SNR value indicates a stronger signal. For example, an SNR of 20 dB means that the signal is 100 times stronger than the background noise.

4. What factors can affect the SNR of an underwater acoustic signal?

There are several factors that can affect the SNR of an underwater acoustic signal, including the distance between the transmitter and receiver, the frequency of the signal, the depth of the water, and the presence of any obstacles or reflections. Additionally, changes in the water temperature, salinity, and turbidity can also impact the SNR.

5. How can SNR be improved for underwater acoustic signals?

There are a few ways to improve SNR for underwater acoustic signals. One method is to use directional transducers that can focus the signal in a specific direction, reducing the amount of noise picked up. Another approach is to use signal processing techniques, such as filtering and equalization, to enhance the desired signal and minimize the background noise. Additionally, choosing a higher frequency for the signal can also improve SNR, as higher frequencies tend to be less affected by noise in underwater environments.

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