I am unclear as to what you want. You said solve for r but you give r as 1000.
In any case r = I/Io and
r = 0.1 antilog (I/Io)
9the max range depends on the sensitivity of the equipment.)
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ExpExchHelpAuthor Commented:
d-glitch:
You're correct... the functions in my XLS converts yards to meters (spreading functions requires meters vs. yards). Anyhow, I looked at the wrong cells (i.e., 1000 yards)... so, again, you're correct w/ respect to "60" and "30".
"To calculate detection range, you need to know the source level and the detection threshold"... here are my questions:
- Could you please elaborate on the thresholds? What input parameters do I need to detect MaxRange?
- WRT frequency, this problem is based on sound (transmission) in seawater.
I welcome any ideas (incl. required inputs) for calculating MaxRange.
**************
aburr:
Thanks for the additional feedback. Yes, I may have not been very clear. I may not always have "r" but know the dB level. So, I wanted to find out about "reverse math"... if I know the dB level, can I calculate "r". Ideally, "MaxRange".
I hope this makes sense.
EEH
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r is not the range
if you you want the range you need to know the initial strength (Io), The max sensitivity of your equip (I) and the attenuation, that is the reduction in signal strength per unit distance.
I think you equations assumed that the signal was reduced because of spreading either spherical of cylindrical. The attenuation of sea water was not included and is not zero.
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ExpExchHelpAuthor Commented:
d-glitch, aburr:
Thanks... initial strength (Io) may vary between 65-100 dB.
Basically, I'm trying to work on a model (submarine listening to "target signals"... e.g., other ships on surface or other submarines).
WTR to attentuation of seawater, I'm using Mackenzie's equation (based on temp, depth, and salinity).
I welcome suggestions for calculating the MaxRange (how far sound can travel given values from other inputs). So, right now, I'm just trying to come up w/ a formula.
>> The value for "r" -- cylindrical spreading -- appears to be incorrect.
You have =10^((10^(I_S/I_D))). It should be =(10^(I_S/I_D))
The detection threshold is apt to be much lower, but it will depend on the equipment (hydrophone, amplifier, etc) you are using.
For example, this is a toy (you can tell because it doesn't list the right sort of specs), but it might have a detection threshold of -10dB. http://www.dolphinear.com/
And if your data is in dB, then you subtract rather than dividing.
So for spherical spreading of an 80 dB signal, you could observe it with -10dB hydrophone at
r = sqrt[ 10^(80-(-10))/10) = sqrt( 10^9) = 31 km = 19.6 miles
This completely ignores the issue of signal to noise.
... the rewriting of the equation to solve for "r", I'm using the following example values:
I_S = 80 db
I_D = 65 db
For spherical spreading, the Excel function will be: =SQRT((10^(I_S/I_D))) = 4.125
For cylindrical spreading, the Excel function will be: =(10^(I_S/I_D)) = 17.013
My question: What's the unit of measurement? Miles? Nautical miles?
Maybe I'm not fully tracking where the "-10dB hydrophone" comes into play.
Look at the value of the Source Level in particular:
SL = 195 dB re . . .
A value in dB is a ratio, not an absolute value.
Since the reference here is in meters, the value for range will also be in meters.
What is reference for your value of Source Level: I_S = 80 dB ?
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ExpExchHelpAuthor Commented:
d-glitch:
Thank you for your continued support on this question... I appreciate it.
I think you're right about the proposed 4 questions. For the current state of this research, I probably want to consider only #1 and #2.
At this time, I'm selecting arbitrary values for testing the calculations.
Assuming, the two example dB values (80 and 65) are valid, I'm trying to get a better understanding on the radius. Although I have limited knowledge on this subject (i.e., sound/sonar), it seems odd that the radius would only be a few meters.
Are potentially other inputs missing? So, if a submarine picks up a signal from a ship (on surface), I'm trying to figure out how far the sound from the "target" (at X level) would travel before the sub cannot hear it any longer.
Here are some additional data and some final sample calculations.
I thought your 65 dB number for the threshold of hearing was way off.
But it turns out the hearing in the air and under the water are measured differently, and the threshold in water is something like 62 dB higher than in air. http://www.arc.id.au/SoundLevels.html
This does make the value you used for the Source Level SL=80 dB somewhat suspect.
This chart suggests that 80 dB is the background level due to wind, waves, and distant ocean traffic. http://www.dosits.org/science/soundsinthesea/commonsounds/
Page 314 in particular:
Small craft and boats and medium-sized vessels (e.g., recreational craft, jet skis, speed boats, operational work boats, hovercraft, support and supply ships, many research vessels, fishing vessels) produce source levels of approximately 160 to 180 dB re: 1µPa, depending on speed and other operational characteristics.
=======================================================================
So, if you assume a small speed boat [SL=160 dB] with transmission loss due to spherical spreading [TL=20*Log(r)] and a detection threshold DT=67 dB and solve for the maximum range:
DT = SL - TL ==> TL = SL - DT = 160 - 67 = 93 dB
20*Log(r) = 93 ==> r = 10^(93/20) = 10^(4.65) = 44.7 km = 27.8 miles
But this is ignoring the ambient noise.
=======================================================================
If the signal is not larger than the background noise, you won't be able to detect it.
If you require a Signal-to-Noise Ratio SNR=6 db and assume a noise level NL=80 dB, then sonar equation becomes:
20*Log(r) = 74 ==> r = 10^(74/20) = 10^(3.70) = 5.01 km = 3.1 miles
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And the calculations are wrong.
20*log10(1000) is 60 (not 59.223)
10*log10(1000) is 30 (not 29.61)
To calculate detection range, you need to know the source level and the detection threshold.
The units will be some form of power per area.
Are you talking about sound or RF or light?