# Combining two decibel values vs dissimilar values

1. Jun 26, 2009

### Alexander100

Hello,

I've got a question to some of you concerning decibels. If you have two dB values...for example, 70 dB's and 75 dB's and both values combine, you don't get a 6 dB maximum improvement.

If we are talking about subwoofers and dB's, I've been told that if you add two identical figures, like 70 dB's + 70 dB's (and the sub's are in phase) that the result would be a 6 dB improvement.

But I've also been told that if two levels are different, that both will not combine to provide with that same 6 dB advantage. So I would like to know from the experienced posters here, why is it that equal levels between both provide an advantage if summed over the dissimilar levels.

Or am I wrong ? I'm not sure so I'm asking anyway.

2. Jun 26, 2009

### Alexander100

I apologize if this is not in the correct forum but I'm not sure which forum I should post in concerning this. I'm sure there are lots of knowledgeable people who can explain this though...

3. Jun 26, 2009

### Bob S

The power measured in decibels, PdB, is equal to the sound amplitude level PA, by the relation PdB = 20 Log(PA). So the dB levels have to first converted to amplitude levels before they can be added. So, adding 75 dB and 70 dB yields:
75 dB: 1075/20 = 5623
70 dB: 1070/20 = 3162
sum = 5623 + 3162 = 8785
Sum = 20 Log(8785) = 78.87 dB
also
75 dB + 75 dB = 20 Log (5623 + 5623) = 81 dB as expected.

The two sound sources have to be at the same frequency and in phase.

4. Jun 26, 2009

### Alexander100

Thanks for the equation ! Some were telling me that two weaker values could not sum to a higher value...that I was defying the laws of conservation of energy !

So ultimately it seems that the level match approach (if in phase) would yield higher total SPL vs gain matching (also if in phase) since gain matching two subs would mean each sub would yield different SPL values per location. Differing SPL levels summed will not offer the benefits that level matching can provide.

Thanks !

5. Jul 28, 2009

### Turv

Alex,

Bobs equations are spot on (in phase).

If they are not in phase then 70db + 75 db would equal:

10 log (10^7.5 + 10^7) = 76.19 db

75 + 75db would equal 10 log (10^7.5 +10^7.5) = 78 db

6. Jul 29, 2009

### turin

Turv, you're mixing two different kinds of dB, namely SPL and SIL (or SWL). The calculations are not comparable.

Alexander, what kind of dB are you using. Your statement that 75 dB combined with 75 dB produces a 6 dB increase implies that you are using SPL.

7. Jul 30, 2009

### Turv

Turin,

Sound power, Intensity or pressure all use the same calculation with regard multiple sources, your need a 4-fold increase in watts to get a 6 dB rise. With pressure you just dont double the Pascals such as 0.2 Pa + 0.2 Pa of which would equal 6dB rise but add the powers in pressure, remember if you the double the pressure then you need a 4-fold rise in intensity so i am correct.

8. Jul 30, 2009

### Turv

Turin,

Just to carry on from my last post as i was in a rush to get to work this morning so i replied quickly.

You state that Spl and SIL (or Swl) are not comparable.

SPL = sound pressure level, IL = Intensity level ( or SWL) is not Intensity but sound power level. I am from the UK so i will use UK terms, SPL is measured in Pascals or N/m^2, Intensity is energy so is measured in Joules per sec with regards surface area, but we usually use W/m^2, sound power is measured in Watts. You say they are not comparable? did you know that Power,Intensity and Pressure are all equal from the source to a distance of 0.282m.

1 Watt of Power = 120 dB

Intensity at 0.282m = 1 Watt/ (4 x pi x r^2) = 1 watt

10 log (1/10^-12) = 120 dB

Sound pressure at 0.282m = SWL - (20 log (distance) + 11)

= 120 - (20 log (0.282) + 11 ) = 120 dB

So how can they not be comparable?

You also state that 75 dB + 75 dB must be SPL if it comes to 81dB, why?, 75 + 75 db IL will also equal 81 dB if in phase.

Lets get some nice round figures to work with, i'll use 80 dB.

80 dB in SPL = 0.2 Pa pressure, so adding 0.2 + 0.2 Pa will not give the answer to two sources that are not in phase, it will not be 86 dB or the Intensity will have to 4-fold and i confess this was a mistake i made about 12 years ago until i consulted experts to clarify the situation.

Two sound sources not in phase 80 dB will be 83 dB so its simply not adding 0.2 + 0.2 Pa, but two sources of 0.2 Pa will produce approx 0.282 Pa.

I hope this clarifies the situation that i am not misunderstanding Power, Intensity and Pressure.

Last edited: Jul 30, 2009
9. Jul 30, 2009

### turin

Turv, I am starting to doubt myself. I am not an expert, but there is something that just does not seem right. Here is my reasoning. If you don't mind, please try to set me straight. I will argue from a different angle.

Let's stick with the comparison between dB(SPL), which measures pressure, and dB(SIL), which measures intensity, which is power per area. It seems that we are in agreement so far about these definitions. (I'm assuming that your lower-case watt is to be distinguished from your upper-case Watt.)

My disagreement is three-fold:

1. dB(SPL) is a logarithm with a factor of 20 whereas dB(SIL) is a logarithm with a factor of 10.

2. Energy is conserved, regardless of whether or not the pressure is in phase, and so the relative phase of the two sound waves is irrelevant for dB(SIL). In particular, if the combination of two 75 dB(SIL) sounds is 81 dB(SIL), then energy conservation is violated.

3. The pressure is not the only mechanism for energy transfer; the acoustic particle velocity also transfers energy. This is a common theme for all wave propagation: the average energy is split evenly between kinetic and potential.

So, 0.2 Pa + 0.2 Pa implies "in phase", that is, double 0.2 Pa. If it is out of phase, then it is not 0.2 Pa + 0.2 Pa, but rather the sum of two lesser pressures. To put it another way, the pressure is time-dependent, and so, when you say 0.2 Pa, it is not clear if you are talking about maximum pressure, instantaneous pressure, or what. However, when you compare to dB(SIL), you implicitly assume rms pressure. The SPL is given as rms pressure, if I'm not mistaken, so it actually doesn't even make sense to combine two dB(SPL) values unless the sound waves are in phase.

10. Jul 31, 2009

### Turv

Turin,

I would seriously doubt myself too! Go and see people that know, i would suggest in the UK.

11. Aug 1, 2009

### Turv

Turin,

Actually i think my last reply was a bit harsh, what i would like to say is this, i don't think that i am an expert in this field but i have a very good understanding of the subject. I will try to answer your disagreement the best i can.

1, dB(SPL) is a logarithm with a factor of 20 whereas dB(SIL) is a logarithm with a factor of 10.

Yes thats correct, but this is because pressure uses Pascals and Intensity uses W/m^2 and i could also argue that they both have different reference levels.

2. Energy is conserved, regardless of whether or not the pressure is in phase, and so the relative phase of the two sound waves is irrelevant for dB(SIL). In particular, if the combination of two 75 dB(SIL) sounds is 81 dB(SIL), then energy conservation is violated.

It is not irrelevant, the sound intensity level of a sound wave is proportional to the square of the amplitude of the sound wave.

Intensity / reference Intensity = (pressure)^2 / ( reference pressure)^2

The result is Intensity and pressure levels are therefore equal.

This may be a bad example but think of resonance, vibration gets worse with other frequencies that are in phase ( sympathetic vibration), what i'm trying to suggest is that the intensity will 4-fold in phase because it is being enhanced (in phase).

3. The pressure is not the only mechanism for energy transfer; the acoustic particle velocity also transfers energy. This is a common theme for all wave propagation: the average energy is split evenly between kinetic and potential.

This is way over my head and i can't comment on the average. :rofl:

I also have a question for you, are you trying to suggest that 2 sources the same dB level not in phase will not be a 3 dB increase but either be zero or 6dB rise?, because that would just be nonsense!

Last edited: Aug 1, 2009
12. Aug 4, 2009

### turin

This is maddening. I believe that you are correct, that I∝p2, which would imply that Δ(SIL)=2Δ(SPL). At the same time, my physics-gut is telling me that two 75 dB(SIL) sounds cannot combine to produce 81 dB(SIL) sound without violating conservation of energy. That is my main objection. Please understand that I do not object to your position, I am just still missing something. I have this sneeking suspicion that I am being very stupid; that I have forgotten something important about waves.

I don't understand what resonance has to do with this. I was thinking, since my last post, that maybe the resolution is in the distribution of nodes and antinodes, which would be a phase issue. I was thinking globally, but perhaps the resolution is for me to think locally.