SPL vs distance... 12 or 6db?

[fonograph]

Does sound pressure  fall off 6 or 12 db per doubling of distance from point source monopole with omnidirectional directivity?

I have read that sound gets 6db( half ) quieter when I double the distance,I also read that sound gets 12 db (quarter ) quieter with doubling of distance if the sound source is point source omnidirectional monopole.

I also read that sound decreases 12 db in near field,and 6db in far field.I also read sound doesnt roll off in near field at all,it just jumps up and down in amplitude with small variations in distancs non-linearly and chaoticaly.

one note,I noticed lots of electronic engineers confused about db when describing sound.It is true that 6db is quadrupling of power,becose 2x voltage will also double current and 2x V + 2x I = 4x power,with sound pressure its different,6db higher sound pressure is double power,not quadruple,keep that in  mind.

[IanMacdonald]

Sound power varies as the inverse square of the distance. Half the distance, four times the power.

The proper sound level unit is the Bel, which is a tenfold increase of sound power. For some reason this got mangled into decibels, which are a tenth of the proper unit. Bels work to a base 10 log law, thus 2 Bels is 100 times the power of 1 Bel, 3 Bels 1000 times, and so on. 

So, halving the distance form the source (in free space) will quadruple the power, but this is less than 10x, so it will be less than 1Bel, or 10dB. In fact it will be the log of 4, which is just over 0.6 of a Bel, x10 if in decibels.  Because negative logs indicate smaller values, doubling the distance instead will cause the same change in a negative direction, or -6dB change.
 
In circuits, power is proportional to voltage squared, so a 1Bel or 10dB increase is given by a voltage increase of the square root of 10, or just over 3x. A 10x increase in voltage gives a 100x increase in power, and that one is easy - 2 Bels or 20dB.

100x (10^2) voltage gain is likewise 10^4 power increase, so 4 Bels or 40dB in sound terms.

As you mention, this only applies when the distances are significantly larger than the size of the radiating element. In the 'near field' you have one of those 'chaotic systems' where conventional maths gets into difficulties.

HTH. The whole thing is made needlessly complex by using an oddball multiplier of the unit. Bit like those people who insist on using hectopascals, dekalitres  or whatever yuckspeak. Why the hell can't they use the STANDARD values? 

[fonograph]

You say bell,or 10 decibel is tenfold increase in power,and while that is true for electronics assuming that current is free to increase due to voltage increase,I think its not true for other things,like SPL for example.,For years I believed 20 db or 2 bell is 10x increase.I read that 6 db = 2x and 20db = 10x,I learned that 20db is one decade,so I believe +20db is 10x sound power.

Can you show me some reputable source that claims 2 bel = 100x sound power?

[dmills]

The proper sound level unit is the Bel, which is a tenfold increase of sound power. For some reason this got mangled into decibels, which are a tenth of the proper unit. Bels work to a base 10 log law, thus 2 Bels is 100 times the power of 1 Bel, 3 Bels 1000 times, and so on. 

Ah, No!

If you are using Bels (which are an inconveniently large unit for most things, hence the decibel being 1/10th of a Bel), then 2 Bels is 100 times the power of a a 0Bel reference, 10 times the power represented by 1 Bel and 1000 times the power represented by - 1 Bel.   

Bels (and by extension decibels) are ALWAYS actually a power ratio and (rather like voltage) doubling the sound pressure level quadruples the power, but the bel or dB are always expressed as power ratios...

Now the surface area of a sphere is proportional to the square of the radius, and conservation of energy says the same total power flows thru a sphere surrounding a point source at any radius (Not quite true for acoustics, particularly at high frequency air is lossy, but go with it), so doubling the distance drops the power per unit area (The power flux density) by a factor of 4, hence 6dB. The pressure level however only drops by a factor of two, but because power is proportional to the square of the pressure, this is also 6dB. 

All of this breaks down in the nearfield where the transducer is no longer an approximation to a point source, and also once you pass the critical distance for the room where the reverberant field takes over. It also fails for things that do not produce a spherical wavefront, which is really a special case of the nearfield condition, you see this with line arrays that produce a cylindrical wavefront (Linear with distance, so 3dB) out to a useful distance for a pop festival, but these are not point sources at designed operating distances.   

Regards, Dan.

[ciccio]

The question is complicated.
In acoustic design it is generally accepted tht the sound pressure level SPL decreases 6 dB each doubling of the distance, but this depends on the geometry of the sound source and of it's surrounding.
A column type speaker (google for "line  array") generates cylindrical waves, not spherical. The attenuation is about 3 dB each doubling of the distance.
Indeed there are specific ratios of frequency (wavelenght) to source lenght to be respected fot this to be true.
You can see line arrays used in major events
They allow for a better coverage of the audience. It depends on the ratio of colum lenght to distance.
A linear type sound source (a road or a railroad) is more similar to a line source than to a point source, and the attenuation over distance is lower.
A point source may be placed on a reflective surface, or against a  a reflective wall or in a reflective corner. The directivity index (DI) will vary and so the attenuation over distance.

Best regards

[Cerebus]

Decibels are just tenths of a Bel in exactly the same way that decimetres are tenths of a metre. We could equally talk about centibels or millibels or decabels or hectobels but in practice we don't. The decibel (dB) is just a convenient size for talking about commonly encountered power ratios, and it's so convenient that decibel has replaced Bel for most common usage. The proper base unit is, however, still the Bel.

• Definition: Bels are a measure of power ratios where power ratio in Bels = log₁₀(measured power/reference power)
• So it follows that: power ratio in dB = 10 log₁₀(measured power/reference power).
  
• If we are talking about power arising from a voltage applied across a fixed impedance R then power P = V²/R.
• So a power ratio arising from a ratio of voltages into a fixed impedance would be ((V_measured²/R) / (V_reference²/R)).
• The R's cancel, leaving us with a power ratio = (V_measured² / V_reference²).
• So from (1) and (5) it follows that the power ratio arising from a ratio of voltages into a fixed impedance, expressed in dB would be 10 log₁₀(V_measured² / V_reference²).
• The usual rules of logarithms means that we can pull the power of 2 outside the logarithm and so:
  the power ratio arising from a ratio of voltages into a fixed impedance, expressed in dB would be 20 log₁₀(V_measured / V_reference).
  

And this is where the frequent confusion arises:-

• A doubling of power in dB is 10 log₁₀(2/1) = 3 dB (properly 3.010299... dB, but it's always rounded off in practice)
• The change in power in dB due to a doubling of voltage (into a fixed impedance) is 10 log₁₀(2²/1) = 20 log₁₀(2/1) = 6 dB (Note the change to 'voltage form')

The latter principle can be extended to ratios of any other quantity that has a quadratic (square law) amplitude to power relationship, which is most scalar field quantities in physics.