Why do modern amplifiers show volume as dB? And what is ??dB?
For a long time, amplifiers had a largish knob that you turn to increase the sound from the system. Just behind the knob on the body, there will be a series of numbers from 0 to say 10 printed like in a clock. The knob will have a small mark on top that will represent what position it is in compared to the numbers. As you turn the knob clockwise, a pot inside will instruct the amplifier to send more power to the speakers. Most of us are used to this way of increasing or decreasing the sound from our system. What does this represent? Power, volume,..... ?
Wattage
A Watt is a unit of measurement that is used to represent amplifier power or the energy output of the amplifier. Let us say we are using a 100 watt amplifier. If we have the knob at position 1 to start with, then move it to position 6, have we increased the volume of sound 5 fold? Actually no, And, that is where ??decibels?? come in.
Decibel
A Decibel is a combination of two words - 'deci' (one-tenth) and 'bel' which is a unit of sound. The word 'bel' is in deference to Alexander Bell who invented the telephone. The human ear perceives sound based upon air pressure exerted on the diaphragm inside the ear. Now there is always some sound around you and this is termed as ambient sound pressure. The extent of a particular sound is measured as a deviation from ambient sould pressure and this is generally represented by a unit called Pascal. There are two sound pressures - Instantaneous, and Effective. Instantaneous sound pressure is the deviation from ambient pressure caused by a sound wave at a given location and given instant in time. Effective sound pressure is measured as Root Mean Square (RMS) square of the instantaneous sound pressure over a given interval of time. The total sound pressure is a sum of ambient sound pressure, and sound pressure deviation. The sound pressure deviation is calculated using two factors - force of air pressure (caused by the sound) and area covered. In wattage this is represented as watts per square meter (watt/sq.meter).
Units of measurement are of two types - absolute and relative. A ??feet?? is an absolute unit as 0 (zero) feet means there is no length at all. Similarly when you say 0 litres of water, it means there is no water at all in the container.
As I said above, sound pressure is always there. The human ear is extremely sensitive and can react to a very large range of sound pressure. Since power of a sound wave is proportional to the square of the pressure, the ratio of minimum pressure to maximum pressure is roughly a trillion! A good ear can actually discern sound that is 0.000000000001 watt/sq. meter!! Now how do you compare 0.000000000001 watt/sq. meter with 1 watt/sq.meter? We can of course say 1 to the power -12, but that is an awkward way for regular use. Thus you use what is called a logarithmic scale.
As we discussed we have two factors - the ambient sound pressure (P(Ref)) and deviant sound pressure (P).
Thus sound pressure level (L) is calculated as follows:
L = 10Log(base 10)*[(P*Squared)/(P(Ref)Squared)] which is equivalent to 20Log(base 10) *(P/P(Ref)). This logarithmic value is represented in dB.
The Log of 1 (watt/sq.meter) is 0dB (zero). The log of 0.000000000001 (watt/sq. meter) calculated as above is -24dB. Now the comparison of these two sound pressure is easy, is it not?
Examples of Deviant Sound Pressure
To give you an idea of what dB represents here are some practical examples:
>> 180 dB << Nuclear explosion at 160 km
>> 150 dB << Jet engine at 30 m
>> 140 dB << Rifle being fired at 1 m
>> 130 dB << Threshold of pain
>> 100 dB << Jack hammer at 1 m
>> 60-80 dB << Passenger car at 10 m
>> 60 dB << TV set at 1 m
>> 40-60 dB << Normal Human voice 1 m
>> 20-30 dB << Very quite room
>> 10 dB << Leaves rustling, calm breathing
Decibel & Volume
As an user how am I concerned with all these? Simple. Wattage does not represent any usable value. A watt, as I said, represents the energy output of an amplifier. Unfortunately the relationship between amplifier output and loudness is not straightforward. If you play an amp at 50 watts, keep everything equal, and play it again at 100 watts, the deviant sound pressure is only 3dB. It generally takes an amplifier with 10 times the power to generate 10dB difference in sound pressure. Why 10dB? Because loudness is subjective and cannot be measured. Loudness can also be different for two different people. So some experiments were done, and it is generally agreed that what people perceive as being 'twice as loud' need an increase in sound pressure of +10dB. And that needs 10 times more power from the amplifier!
So next time you are listening to some music as 50dB, and then increase it to 60dB, remember you are now listening at twice the previous volume.
OK. But What is Minus dB
As I said before, there is sound all around us all the time. Unless you are living in perfect vacuum, there is no such thing as 0 (zero) sound pressure, and cannot be measured in absolute terms. To measure sound pressure deviation, we need to set a base level. In the audio industry, the base level has been set at 20 micro Pascals, which is considered to be at the threshold of human hearing. In addition this is also calculated at 1000Hz or 1Khz. Most measurements of audio equipment are made relative to this base level that is set at zero (0dB). In comparison a Jack Hammer at 1 m will be roughly 2 Pascals and 100dB. Since the base level is not an absolute zero, you will be able to hear sounds that are less than zero or negative. And these are represented as Minus xxxdB (-xxxdB)
Cheers