How does the decibel scale work?

Answer 1

The decibel scale is a "logarithmic" scale, meaning that in order to move up by the same amount from any starting point, you don't add the same amount, you multiply by the same amount.

For example, if I increase the loudness of my harmonica from 1 watt to 2 watts, while you crank your Electric Guitar up from 1,000 watts to 2,000 watts, both of us doubled our original sound power, and increased our sound by the same number of decibels.

It's important to understand that the number of decibels always means the size of the change from the original amount. Some number of decibels is not a quantity that you can hold in your hand. It's always a comparison between the original and the final. When you see a number of decibels stated, the original value is always lurking somewhere nearby, or else it's clearly understood.

Increasing the original power means adding dB. Decreasing the original power means subtracting dB (or adding negative dB).

Multiplying the original power by 10 is an increase of 10 dB. Dividing the original power by 10 is a decrease of 10 dB.

Technically, the way to calculate the dB of change is

dB = 10 times the log of [(new power) divided by (old power)].

Some quick and easy approximate numbers to remember, so you don't have to calculate it every time:

Multiply or divide by 2 ==> plus or minus 3 dB

Multiply or divide by 4 ==> plus or minus 6 dB

Multiply or divide by 5 ==> plus or minus 7 dB

Multiply or divide by 8 ==> plus or minus 9 dB

Multiply or divide by 10 ==> plus or minus 10 dB (definition)

Example:

-- Increase power from 1 watt to 40 watts ==> Multiply power by 40.

x 40 = product of (10 x 2 x 2) = +10dB + 3db + 3db = +16 dB.

This is exactly the same as the change from 1 billion watts to 40 billion watts ... still +16dB, because it's the changethat counts in dB.

-- Decrease power from 100 watts to 25 watts. Divide 100 by 2 (get 50), then divide 50 by 2 (get 25).

Divide by 2 the first time ==> minus 3 dB. Divide by 2 the second time ==> minus 3 more dB.

So 25 watts is 6 dB below 100 watts.

When referring to the standard decibel scale as a measurement of the intensity of sound, it is important to note that 0 dB is set at 10-12W*m^(-2). In the above equation for dB, if you are using the standard scale, always use 10-12 as your (old power) value.