For acoustics, 0dB often means thethreshold of hearing, 0.0002ubar (Microbars: a bar is the "normal"pressure of air). The standard level (0dB) is chosen to besome convenient value for the application. The question "relativeto what?" has no single answer. The final confusion comes from the concept of RELATIVE power. Power of sound varies as the square of pressure, so this formula is alsoappropriate for SPL (sound pressure level) calculations. Squaring avalue doubles its logarithm, so our dB formula becomes: Most often wemeasure voltage and use the formula P=E squared over R to get power. Power is notoften conveniently measured, especially in electronic devices. Remember that the dB is used to describe relationships of POWER. Converting voltage or pressure ratios to decibels If we merely double the power (3dB), the difference will bejust noticeable. If a sound has 10 times the power of a reference (10dB) we hear itas twice as loud. Inthe second place, our judgment of relative levels of loudness is somewhatlogarithmic. meter and thethreshold of pain is around 1 watt/sq. The softestaudible sound has a power of about 0.000000000001 watt/sq. The usefulness of all this becomes becomes apparent when we think about how theear perceives loudness. If we measured one value as 23 hp and anotheras 4.7 trillon hp, we say that one is 113dB greater than the other. Aslong as we are going for simplicity, we might as well get rid of the decimal, sowe multiply the number times ten. For convenience, we find the RATIO between the twonumbers and convert that into a logarithm. Wecould use scientific notation, but a comparison between 2.3 X 10 and 4.7 X 10 tothe 12th is still awkward. With such vast differences between thenumbers, the most difficult problem is getting the number of zeros right. They never change.) Adecibel is a RELATIONSHIP between two values of POWER.ĭecibels are designed for talking about numbers of greatly different magnitude,such as 23 vs. (You can go to the National Bureauof Standards and look at a foot or a dyne if you want to. Dynes and feetare defined quantities of force and distance. The decibel is not a unit in the sense that a foot or a dyne is. Although the term decibel always means the same thing, decibels maybe calculated in several ways, and there are many confusing explanations of whatthey are. The decibel (abbreviated dB) must be the most misunderstood measurement sincethe cubit.
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