Decibel

Perceived levels of sound, and of phenomena such as radio and light signals, change according to logarithm of actual power level. Units have been invented to take this in the account.

The fundamental unit of sound change is called as decibel, often represented as  dB. A change of 1 dB is minimum increase in sound level which you can detect, if you are expecting it. A change of   1 dB is minimum detectable decrease in sound volume, when you are anticipating change. Decreases in volume are negative values and increases in volume are positive decibel values.

If you are not expecting the level of sound to change, then it takes around 3 dB or -3 dB of change to generate a noticeable difference.

Calculating decibel  values

Decibel values are calculated according to logarithm of ratio of change. Assume that a sound produces a power of P watts on your eardrums, and then it changes to a level of Q watts. The change in decibels can be obtained by dividing out the ratio Q/P, taking the base-10 logarithm, and then multiplying it by 10:

dB = 10 log (Q/P)

As an example, assume that a speaker emits 1 W of sound, and then you turn up the volume such that it emits 2 W of sound power. Then P = 1 and Q = 2, and dB = 10 log (2/1)=10log 2 = 10*0.3 = 3 dB. This is minimum detectable level of volume change if you are not expecting it: a doubling of actual sound power.

If you turn down the volume level again, then P/Q = 1/2 = 0.5, and you can compute dB = 10 log 0.5 = 10 × -0.3 = 3 dB.

A change of plus or minus 10 dB is an increase or decrease in sound power of 10 times respectively. A change of plus or minus 20 dB is hundredfold increase or decrease in sound power. It is not unusual to encounter sounds which range in loudness over plus or minus 60 dB or more-a millionfold variation.

Sound power in the terms of decibels

The above formula can work inside-out, so that you can determine the final sound power, given initial sound power and decibel change.

Assume that the initial sound power is P, and change in decibels is dB. Let Q be the final sound power. Then Q = P antilog (dB/10).

As an instance, suppose initial power, P, is 10 W, and change is 3 dB. Then final power, Q, can be given as Q = 10 antilog (3/10) = 10 × 0.5 = 5 W.

Decibels in real life

A volume control potentiometer may have a resistance range such that you can adjust the level over about plus or minus 80 dB. The audio taper ensures that the decibel increase/ decrease are a straightforward function of rotation of shaft.

Sound levels are specified in decibels relative to the threshold of hearing, or the lowest possible volume a person can detect in a room, assuming that their hearing is ordinary. This threshold is assigned value 0 dB. Other sound levels can then be quantified, as a number of decibels like 30 dB or 75 dB.

If some noise is given the loudness of 30 dB, it means it is 30 dB above the threshold of hearing, or 1,000 times as loud as quietest detectable noise. A noise at 60 dB is 1,000,000 times more powerful as the threshold of hearing. Sound level meters are used to determine dB levels of several noises and auditory environments.

A conversation may be at the level of 70 dB. This is 10,000,000 times the threshold of hearing, in the terms of actual sound power. The roar of crowd at the rock concert may be 90 dB, or 1,000,000,000 times threshold of hearing.

A sound at 100 dB, typical of the music at a large rock concert, is 10,000,000,000 times as loud, in the terms of power, as a sound at threshold of hearing. If you are sitting in the front row, and if it's a loud band, your ears may get wallopped with peaks of 110 dB.