The Decibel Scale

Decibel is literally one-tenth of a bel. The bel is named after Alexander Graham Bell. A bel is the ‘logarithm of a ratio’ of any two sound (or electrical) intensities. Thus,

1 decibel = 10 bel = 10 Iog₁₀ (ZZZ₀)

where I is the intensity of sound which we want to measure, and

I₀ is the intensity of reference sound.

The bel had its origin in the Bell Telephone Labs where it was used as a convenient way to express power losses in telephone lines as power ratios. Thus, decibel is log of the ratio of two powers. It was originally called the ‘transmission unit’ or TU by the bell Labs people.

Although decibel is used to measure sound level, it is also widely used in electronics, signals and communication.

If the ratio between the powers (P₁ and P₂) of two sounds is two, then the difference in dB is 10 log (P₂∕P₁) =10 log 2 = 3 dB.

Similarly, if the power of second sound were 10 times the first, then the difference in dB would be 10 log (P₂∕P₁) = 10 log 10 =10 dB.

Note that the decibel scale is logarithmic and each 10 decibel increase means 10 fold increase in noise intensity. A 10 decibel increase is perceived as the doubling of loudness. Thus, if we compare sounds of 20 and 30 decibels, then the 30 decibel sound is 10 times more intense and has double loudness as compared to 20 decibel sound. Similarly, if we compare 20 decibel sound with 40 decibel sound, then we find that 40 decibel sound is 100 times more intense and has 4 times more loudness as compared to 20 decibel sound.

The lowest sound that the human ear can detect is 0 dB. It is also the threshold of hearing. But what does 0 decibel mean? When the intensity of sound to be measured is equal to that of the reference sound, then

10 log 7₂∕7₁ = 10 log 1 (when I₁=I₂)

= 0 dB (since log 1 is 0)

Thus, 0 dB does not mean that there is no sound.

A soιmd of 0 dB corresponds to 0.02 m Pa pressure. This is a very low pressure and is 2 ten billionth of an atmosphere.

The human ear does not respond to all frequencies equally. It is more sensitive towards the frequency range of 1000 to 4000 Hz as compared to very low or higher frequencies. Thus, sound meters are fitted with filters having responses similar to human ear. If the ‘A weighting filter’ is used, then the sound pressure level is given in dB (A) or dBA units. These units are widely used because sound pressure level is easy to measure in dBA scale. The other filters such as B or C type are also used which yield dBB or dBC scales of measurement.

The decibel levels of some familiar sounds are given in Table 11.1.

Table 11.1 Some Common Sounds and their Characteristics

11.5