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 and we shall learn this in the later part of this lecture. 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…
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!
Frequency Mix/Profile & Loudness
Case Study: His 20W amp is Louder than My 20W, hence Marshall is Louder than Fender!
We have learned that any sound other than pure sine wave is a mixture of low frequencies, some mid frequencies & some high frequencies, often generalised as Bass, Mid & Treble.
Human ear is not uniform when it comes to sensing different frequencies at the same level or same power. Inherently or naturally, human ears are more sensitive to mids, compare it with fact that vocal range or our speech is the middle region of audible frequencies and GOD has designed our ears to be the most sensitive to these frequencies. This also means that a boost in these frequencies will be perceived as very high increase in loudness or even piercing as the ears are most sensitive for middle range of frequencies. This is also the prcise reason why we tend to like HIGH BASS, HIGH TREBLE and LOW MIDS… recall that party beat.
There is indeed an experimental study done by 2 people named Harvey Fletcher and Wilden A. Munson in 1933 which shows and proves this fact.
Fletcher Munson Curve
Just a quick look at this diagrams which is a equal loudness curve shows that for the same loudness level at any level, the mids decibel are the lowest and lower frequencies are highest. Hence this also means that,
…a balanced sound will have a much higher Bass, Slightly lower Treble & lowest Mids.
Lets come back to the case study and explain!
We are talking about a Guitar amplifier and the case is “our Guitarist” is making an assumption that for the same power & type one brand of amplifier sounds louder than other. TWO pretty subtle things are happening here…
1. A guitar is an instrument which has middle range sound, we just learned middle region being the most sensitive to human ears.
2. Also for same power rating and design type of amplifiers, there are always subtle trademark tone shaping “preamp” sections in them
It is because of exactly this, the overall tonality of amps which is governed largely by the preamp in them becomes different, obviously this is the reason why despite having same output power one amp appear louder than the other…. NOTE THAT it just APPEARS louder, actually its NOT!
Don’t judge by what you perceive, each amplifier has its own character an identity an individuality!