THE DECIBEL SCALE - UNDERSTANDING SAFETY NOISE

A sound consists essentially of a moving series of pressure fluctuations, and the normal unit of pressure is the pascal (abbreviated to Pa). However, it is not normal to measure sound in pascals; instead the decibel (abbreviated to dB) scale is used.

The decibel scale is a logarithmic one, which compresses a large range of values to a much smaller range. For example, the range of sound pressures from 0.00002 to 2.0 Pa is represented on the decibel scale by the range 0 to 100 dB. Two justifications are normally given for using a decibel scale.

1. The range of values involved in measuring the amplitude of sound is inconveniently large.
2. The human ear does not respond linearly to different sound levels and the decibel scale relates sound measurement more closely to subjective impressions of loudness.

Neither of these explanations really stands up to scrutiny. We cope with larger ranges of values when measuring other quantities (length and money are just two examples of this). It is certainly true that our ears do not respond linearly to changes in sound pressure. In other words doubling the sound pressure does not double the apparent loudness of a sound.

However, they do not respond linearly to the decibel scale either, so little has been gained in this respect by using a decibel scale. Whatever the original reasons for adopting a decibel scale, it is now used universally, so there is no alternative but to do so.

The use of a logarithmic scale dates from the days before electronic calculators when many calculations were carried out with the help of a book of logarithms, or ‘log’ tables. As a result, logarithms were much more familiar to anyone who needed to carry out calculations regularly.

Many fewer people are nowadays familiar with them. Fortunately, with the help of a calculator, decibel calculations can be carried out without any great understanding of how logarithms work.

In other fields, different logarithms – called natural logarithms and abbreviated to either loge or ln – are used.

In workplace noise calculations, all logarithms will be the more familiar system based on the number 10. They are sometimes called ‘logs to base 10’, abbreviated to log10, log or simply lg.