decibel

[DF96]

Anything with a reasonable automatic gain control system is likely to end up with something like a logarithmic response if it has to cover a wide range of input amplitudes: ears, eyes, radio receivers.

 

[SY]

But nonetheless, as you said before, it's principally for calculational convenience, much like pH in chemistry or absorbance in optics, which are unrelated to human sensory response.

 

[nattawa]

Because the ear is logarithmic in its response.

This means we can hear a huge range of sounds.

You did not answer the question "Why logarithm?", and no one can so far, hence "God knows" still stands.

IMHO you took it backwards. Human perception to many physical quantities is neither linear nor logarithm exactly nor exactly any other mathematical modeling. Since logarithm was found in many circumstances to be the least inaccurate modeling among all and to be easy to understand and operate, it has become widely used when people trying to deal with physical quantities' associtation with human perceptions.

"Huge" range of sound human can hear? I've been disappointed for the range of human hearing being too poor, and our music, our symphony orchestras has been too small and simple.

 

[DF96]

We have told you exactly why dB uses logarithms. It is simply a matter of mathematics.

Why is our hearing etc. logarithmic? Because that is the way to get a uniform response to a wide range of input amplitudes. We have also said that. Any other response law gives responses which vary with amplitude, which could be a disadvantage. Whether we got this from God or Nature is off-topic for this forum.

I'm not sure whether it is the mathematics of logarithms or the mathematics of gain control systems which is troubling you.

 

[kevinahcc20]

The human ear responds to a wide range of SPL because you are more likely to survive if you hear danger approaching from a long distance making very little noise, but it also helps if you can continue tracking the threat that runs faster than you, getting closer and louder until its crashing through the trees right behind you...LOOK OUT!!!!

 

[cbdb]

Compare a linear volume pot and a logrithmic volume pot and see which seems to change the volume more smoothly.

All volume meters are logrithmic.

We also hear tone logrithmicaly and so our music is based on octaves.

My guess is that its the only way evolutuion can squeeze in such large dynamic ranges. (120 db is a million times more power than that mosquito)

 

[Peckerwood]

That is right. When an audio tapered pot used as a volume control is on 5 it sounds half as loud as it does on 10 but it is not half the value in resistance. A linear tapered pot used as a volume control (which is not often done) will be double the value of resistance on 5 as it is on 10 but it won't sound half as loud.

 

[CBS240]

Human ears have also evolved to detect differences in phase. Possibly has something to do with the reason phase and intermod distortions are so audiable, wrt harmonic distorions. From the survival POV, this allows us to judge distances from different sounds and with 2 ears, give us a 3D aural perspective. Why do you think we have 2 eyes instead of one? Stereo!!

 

[Nico Ras]

the dB is used to linearize an exponential value and makes it a simple quantity to work with.

Take an example, what is the attenuation of some transmitted power related to an observer some distance D the source.

Now you do not know the power so make it zero dB which has no relation to the actual power but it is relative, besides that if it was a point source the power measured at some distance D from the source is quite difficult to do in your head, because first of all you would calculate the surface area of the sphere some distance D from the source.

So it would be a lot easier work with the dB and if you do all the division and multiplications in your head this is going to be some feat. If the distance is zero obviously the reference is zero dB or no attenuation, if the distance from the source is doubled then the attenuation is 6 dB, doubled again it is 12 dB.

Now let us assume that the radiating source is directional, i.e. it radiates in 180 degree solid angle, in other words instead of the power at the source being 0 dB it is doubled and is 3 dB higher that it would be with a omni directional point source.

Obviously at the same distance D the power will now be -6 dB (the attenuation) +3db the antenna gain equals -3dB and half the relative power reaches the observer.

Again let us assume that you have some form of capturing device such as an antenna with gain of 1 dB, then the ratio of receiver power over transmitted power is -2dB at the observer.

Now try and calculate all these quantities using PI, D Gain at either side and squaring values in your head.

You use an audio taper pot to linearize the position of the setting with the ear's response to loudness. An audio taper pot is a logarithmic approximation of the voltage divider or attenuation function.

 

[DF96]

If you double zero distance you still get zero distance! You need to start from a reference distance, not zero distance. Then you have something to double.

 

[Nico Ras]

How does one double zero distance? If the distance is zero and you quadraply it it is still zero, you are still at the source or reference point, so what exactly is your remark aimed at?

 

[Nico Ras]

DF, Have you tried taking the Log of zero, what do you get?

 

[AndrewT]

Now you do not know the power so make it zero dB which has no relation to the actual power but it is relative, besides that if it was a point source the power measured at some distance D from the source ......................... If the distance is zero obviously the reference is zero dB or no attenuation,

this part causes the problem.

The reference signal strength will be at the reference distance, not zero distance.

 

[DF96]

If the distance is zero obviously the reference is zero dB or no attenuation, if the distance from the source is doubled then the attenuation is 6 dB, doubled again it is 12 dB.

This is the bit which starts from zero, then doubles it.

 

[kbeist]

Please correct me if I am wrong:

Doubling distance of the reference, the Db also needs to be doubled?

I thought it was a log function.

 

[SY]

Please correct me if I am wrong:

Doubling distance of the reference, the Db also needs to be doubled?

Doubling distance means SUBTRACTING 6dB.

 

[DF96]

If you have free space propagation, then doubling the distance adds 6dB to the attenuation (=power flux per unit area is a quarter). Doubling the distance again adds another 6dB (=-12dB). Doubling again (to 8 times the initial distance) adds another 6dB (=-18dB). So doubling the distance does not double the dB, it just adds 6dB.

Different rules apply if it is not free space propagation (e.g. with reflections, absorbing medium, transmission line).

What about going the other way - getting closer? Halving the distance reduces attenuation by 6dB (power up by factor of 4) etc. etc. This continues while free space propagation holds. It does not hold when you get too close to the source, the power then goes up more slowly. If this were not so you would get infinite power when you touch the source.

 

[kbeist]

Thanks much for the clarification!

Synopsys: Doubling distance = doubling attenuation

 

[Nico Ras]

That is correct DF96, for every doubling of the distance the attenuiation is 6 dB higher propagation loss and it is easy to calculate in your head 6 + 6+.... attenuation instead of using complex calculations. That is why we use dB, it is simpler. I think this was the original question that was asked.

 

[Cal Weldon]

Thanks much for the clarification!

Synopsys: Doubling distance = doubling attenuation

You'll get into less trouble if you simply remember that for every doubling of the distance you subtract 6dB as others have said.