# decibel

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#### Professor smith

I learned that the decibel is a relative value. I don't understand why it's often used to refer to loudness or signal levels. I dont understand why logarithm is used. You often hear that 3db = double loudness. What does that mean?

How does the decibel work in electronics and sound pressure levels?

#### nattawa

.....You often hear that 3db = double loudness. What does that mean?

How does the decibel work in electronics and sound pressure levels?

If memory serves 3db does not mean perceived double in loudness, but a barely distinshable change in loudness for an average human, which also means double/half in power.

Why logarithm? God knows. We were not created with sensations to lineally respond to physical quantities, loudness, sound frequency, brightness, and so on. Perhaps logarithm is one of the better ways to associate our sensations with physical quantities than a lineal system?

#### DF96

Those overseas may not realise that the teaching of logarithms in UK schools has deteriorated somewhat since we started using pocket calculators, so a whole generation now lacks the practical experience of logs which us old'uns have. When you have used log tables to routinely carry out multiplication in, say, a chemistry lab you get an understanding of them which makes decibels much easier to grasp.

#### RJM1

Actually 10db is twice/half the perceived loudness, 3db is twice/half the power, 6db is twice/half the voltage and one db is the minimal sound difference discernable by the average human ear.

#### AndrewT

a decibel is a tenth of a Bel.
A Bel, is a ratio, for this "relative to" can be understood as meaning the same in respect to the reference.

3dB = 0.3Bel
That is exactly the same as saying the ratio is 2:1, whereas -3dB is a ratio of 1:2

In electronics the reference will be stated or sometimes is understood by definition.
eg. dBV is relative to 1V
dBm is relative to 1mW into 600r
dBu is relative to 0.7747V
dBW is relative to 1W

Be careful with mixing up voltage and power. These are treated differently.
Power ratio in dB is {10 * Log (P1 / P2)}
Voltage ratio in dB is {20 * Log (V1 / V2)}

dBSPL is sound pressure relative to a reference.
Usually this reference is the physical pressure just at the threshold of human hearing. It is defined in precise terms as xPascal.
According to Wikipeadia the threshold of human hearing at 1kHz is 20uPa rms. This is equivalent to 0dB 1kHz.

At other frequencies the 0dB (threshold of hearing) reference pressure will be different.

Log is used because the Scientists and Physicists before us decided the best way to express this ratio was to use the formulae, as defined, so that all of us can understand where we are all at.
You do not need to know why they chose logarithms, simply accept that is what they decided so we can universally talk/write to each other without ambiguity.

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#### DF96

dBm is relative to 1mW, whatever the impedance. It may be 600R for audio, or 50R for radio.

Log is used for expressing ratios because most humans used to find adding to be easier than multiplying. Now that many humans are equally baffled by both, it may be time to stop using dB!

#### lineup

I knew it originated from Alexander Graham Bell.
Any unit we use has got his 'old father' and uses his name.
Eventually, international standards bodies adopted the base-10 logarithm of the power ratio as a standard unit,
named the bel in honor of the Bell System's founder and telecommunications pioneer Alexander Graham Bell.

#### Fogonazo

Some information:

#### Attachments

• Decibel.pdf
68.1 KB · Views: 116

#### DF96

That article from Elektor is a useful summary, but it contains a couple of mistakes. Firstly, dB is simply a ratio between two quantities - one of them does not have to be some "clearly defined and indicated reference level". That is why you can specify amplifer gain in dB.

dBm is relative to 1mW - no impedance needs to be specified unless you want to calculate a signal voltage. So 3dBm in a 600ohm circuit is exactly the same power as 3dBm in a 50ohm circuit: 2mW.

dBu is 0.775V, which just happens to be 1mW into 600ohms.

The article says, correctly, that dB for voltage and power are worked out differently but it doesn't say why. It is because power is proportional to voltage^2.

#### bob91343

Notwithstanding all the mostly correct comments, the original poster didn't get his question answered. So I will answer it.

The decibel is, indeed, based on a power ratio. However, in terms of sound intensity, this idea has been corrupted and so when someone says "120dB of sound will damage your ears" he is assuming that you know the reference.

The reference is what has been assumed to be the quietest perceived sound. Frankly, I don't know the figure in sound pressure but that should be available somewhere on line. I too agonize over the sloppiness of this kind of thing but what's a person to do about it?

#### sklimek

The reference is what has been assumed to be the quietest perceived sound. Frankly, I don't know the figure in sound pressure but that should be available somewhere on line.

From the Wiki article from the above link -

dB(SPL)

'dB (sound pressure level) – for sound in air and other gases, relative to 20 micropascals (μPa) = 2×10−5 Pa, the quietest sound a human can hear. This is roughly the sound of a mosquito flying 3 metres away. This is often abbreviated to just "dB", which gives some the erroneous notion that "dB" is an absolute unit by itself. For sound in water and other liquids, a reference pressure of 1 μPa is used.[16]'

I wished I could of witnessed that experiment go down...

Then there are those of us who just never warmed up to Pascals and still use 0.0002 dynes/cm^2 as the reference level.

Don't forget the various weighting curves that can be applied to make measurements more closely resemble human hearing, or for other purposes- A weighting, C weighting and several others. You'll commonly see dBA, which discounts the lower frequencies. IMO, the best site to explain weighting is a UK site, diracdelta

#### Peckerwood

The actual reason logarithm is used is because human hearing is believed to be logarithmic rather than linear. It probably is too but I don't know how that could ever be proven. I think it is obvious that it is more logarithmic than it is linear though.

#### DF96

No. Decibels use logarithms because decibels are about ratios, and logs let you handle ratios by adding/subtracting instead of multiplying/dividing. For people doing mental arithmetic (e.g. engineers over 40 years old) adding is easier than multiplying.

If you want to talk about ratios of sound intensities then decibels are an obvious way of doing it.

In addition, it turns out that our hearing is roughly logarithmic in response. This makes dB even more useful, because they roughly correspond to our perception. They could still be used if this were not the case, so this is a bonus not the main reason.

#### Nico Ras

No. Decibels use logarithms because decibels are about ratios, and logs let you handle ratios by adding/subtracting instead of multiplying/dividing. For people doing mental arithmetic (e.g. engineers over 40 years old) adding is easier than multiplying.

I object to this statement unless you meant that engineers younger than 40 could not even add or subtract without using a calculator.

#### DF96

Sorry if it offends you, but I have seen too many UK students using calculators for simple arithmetic (and even then sometimes getting the wrong answer). Maybe it is a UK-only problem?

#### AndrewT

(and even then sometimes getting the wrong answer). Maybe it is a UK-only problem?
in Scotland we can do a bit better than "sometimes", we're moving towards "usually".

I was astounded recently when I was sitting opposite a pupil and she was doing all the arithmetic in her head. It's a rare ability today.

#### AKSA

This problem appears to be extant in the English speaking world. It's rampant in Oz too, and I noticed it in the US as well. People would be surprised I could do simple calculations in my head. It's a generation thang.....

#### nigelwright7557

Why logarithm? God knows.

Because the ear is logarithmic in its response.

This means we can hear a huge range of sounds.

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