# Relationship between gauss and decibels

In my ongoing effort to understand the world around me, I want to wrap my head around the relationships between two units of measure. Specifically gauss and decibels.

The quandary comes from my understand of waves. Hertz is the measure between wave peaks and describes the frequency of the wave. And from what I know about sound, decibels is the measure of intensity. I've played around with a spectrum analyser designed for sound and really got an understanding of how it all works.

Then I turned my attention to electromagnetic waves. I was looking for a tool that I could use to measure electromagnetism at any given location. The first tool I came across was an electromagnetic field meter (EMF meter) which is measured in gauss. Wouldn't it be equally effective to measure in decibels?

I also could not find a conversion from one to another, so I would assume they measure different things. Can you clear this up for me?

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The Gauss is a measure of magnetic field strength. If your tool is described as a EMF meter then someone is playing fast and loose with their terms somewhere. Secondly, decibels are used to describer relationships between wave amplitudes in electrical engineering, but don't make a lot of sense for describing absolute amplitudes. I'll leave it so someone with more practice in these matter to write a full answer. –  dmckee Apr 24 '12 at 21:16
Decibel is useful for anything, not only for wave amplitudes. See en.wikipedia.org/wiki/Decibel and if necessary, I'll do the answer, but tomorrow. –  Pygmalion Apr 24 '12 at 23:05
@Pygmalion: It's the logarithms that are useful. Sticking the "decibel" label is just habit, and one that is ignored in field where there was a preexisting logarithmic scale such as earthquakes energies or the brightness of objects in the heavens. –  dmckee Apr 25 '12 at 1:39
Is this still open, requiring the answer? –  Pygmalion Apr 25 '12 at 21:24
@Pygmalion: yes, please answer. I think the flaw might be in my understanding of waves vs fields. I assumed a field is just the effective area of a wave before it is completely degraded. –  Jacks_Depression Apr 25 '12 at 23:01

In some natural science fields physicists/engineers are faced with physical quantities, which values can span several orders of magnitude. In such situations, writing values is very cumbersome, especially if they are used in everyday life.

A good example is intensity of the sound. Generally, sound intensity that is audible by human ear spans over 10 orders of magnitude. In order to make a practical notation a logarithmic scale is very useful.

Bel (B) is simply defined as a 10 base logarithm of ratio between quantity $Q$ and its reference value $Q_0$.

$$\text{B} = \log_{10} \frac{Q}{Q_0}.$$

$Q_0$ must be properly defined within particular engineering/scientific community. Usually decibel (dB) is used

$$\text{dB} = 10 \; \log_{10} \frac{Q}{Q_0}.$$

Decibel can be used for any imaginable physical quantity: in my work I have used decibels to measure such diverse quantities from intensity of the sound to amplification of electronic circuits.

Logarithmic notation is also very useful for calculating multiplications, since they are turned into additions, e.g. if you have multistage electronic amplifier, you simply add up amplifications of individual stages. Adding may be more tricky, but for most common cases you get used to, e.g. if you have two equal sound sources, intensity of both sources is increased by

$$10 \; \log_{10} \,2 = 3 \, \text{dB}.$$

Gauss is on the other hand an (obsolete) unit for measuring magnetic field strength. I have never heard that decibels are used for magnetic quantities, but it is possible. It depends on the definition, because you must know reference value in order to use them.

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