POWER & LOUDNESS
The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth (deci-) of one bel, named in honor of Alexander Graham Bell; however, the bel is seldom used.
Human ear are inherently non-linear in nature. With increasing volume level the sensitivity of the ear decreases. In other words, at lower levels a slight increase in level appears more increase than by same amount at higher levels. This behaviour is mathematically represented by Log scale which has the property that with increasing level the rate of increase keeps decreasing. This is also the precise reason why the Volume Pots (Knobs) are called Log pots which are designed with increasing rate to counter the non-linearity of human ear and hence providing a constant apparent level increase on the turn of the knob.
For the sake of better understanding of wider audience, I’ll try to explain the concept of logarithm as well.
We know that 10 squared is 100, or 102 = 100. This can also be re-written logarithmically as Log (100) = 2. Similary, Log (1) should be 0, because, 100 = 1.
This means that Log (100) is 2 units more than Log (1), now pay atention to the fact that, 100 is 100 times 1 but if you apply log it just shrinks.
Its important to understand this representation of the relation, this is the core concept of logarithm.
Coming back to the Decibel, the relation between decibel and power is given by following relation:
Decibel or DB = 10 x Log (P⁄P’) here P’ is reference power.
This also means that DECIBEL is a RELATIVE measure. It always means Loudness level relative to a certain reference.
After a short lesson on mathematics lets get to business busting some myths…
Myth #1: Case Study: Higher wattage lead to Higher Loudness
A guitarist ready for some rock n roll action is depressed that he has got just a 10w tube amp not rocking enough for the bigger gigs which have started happening these days. Finally he decided to knock it off and go for a double sized 20watter amp. He brings it over to his jam room and craks up the levels, just to add to his frustration, it was only marginally louder. 🙁
What actually has happened is Mr. Mathematics had just rocked harder! 😛
Lets get back to how we defined Decibel – It is 10 times Log (P⁄P’). Here the new amp is 20W and the older one was 10. So our decibel becomes, 10* Log (20⁄10) = 10* Log2 =10 * (0.30) = 3 Decibel. We now know that by doubling the power only 3 Db increase in perceived loudness occurs.
BUSTED MYTH: Doubling Power doubles Loudness!