Logarithms (or logs for short) are simply a way of describing numbers which vary by very large amounts in a much smaller range. Just about every piece of audio equipment (microphones, loudspeakers, sound cards, amplifiers, mixers, etc) will have specifications expressed as logarithms (i.e. So, for instance, a twenty decibel sound is ten times louder than a ten decibel sound, and represents a hundred point jump up the decibel scale (10x10100). Each step up the decibel scale represents a doubling of the total sound pressure levels. We need to get familiar with the idea of a logarithm. Sound decibels are known as dB SPL or the Decibel Sound Pressure Level. Other variations that may be seen are dB A or dBA. These symbols are often used to denote the use of different frequency weightings used to approximate the human ears response to sound, although the measurement is still in dB. There are also dB (B), and dB (C) weightings. The decibel is a better fit to how our brains perceive sound. The dB (A) scale is an adapted dB scale - it gives relative measurements. The relationship between perceived loudness and the decibel is a straight line. On the next graph below, a logarithmic decibel scale is used and now the curve becomes a straight line.
Our ’10x’ rule means that as the overall level increases, we need increasingly large changes in intensity to get a similar change in loudness. An intensity of 1,000 is also half as loud as an intensity of 10,000. So an intensity of 1,000 is twice as loud as an intensity of 100. To make a sound twice as loud, you need to multiply its intensity by about 10. You must first antilog each number, add or subtract and then log them again in the following way: For example, adding three levels 94.0 + 96.0 + 98. In the graphs below, the x-axis represents the perceived loudness of a sound, and the y-axis represents the acoustic intensity needed to create that loudness. Sound levels are generally expressed in decibels, which are logarithmic and so cannot be manipulated without being converted back to a linear scale. After analysis, I could offer various recommendations to rectify the issue − all distinctly individual from each other, as acoustics can be affected by nearly everything!” Rob Bungay, Acoustic Consultant, WSP What are decibels? To understand and try to reduce these causes of complaints, among other things I installed sound level meters throughout the room to record noise levels during the day and night, and used acoustic models of the space to assess changes within the room. “I recently worked on a multi-bed intensive care ward where patients and visitors were complaining about the intrusive noise made by the alarms from bedside monitors.
In acoustical and audio engineering, decibels are used everywhere because knowing how loud a sound is important whether you’re assessing whether the noise from a new road is going to be a problem or setting the loudness of music in an arena. Graphic: Nick Maroulis Where are decibels used? When a sound is perceived to double in loudness, this corresponds to roughly an increase in 10 dB. It makes things easier if a logarithmic scale is used this is what the decibel scale is. The ratio of intensities between silence and ‘ow that hurts my ears’ is about 1:100 million million. The human ear is capable of hearing very quiet (low intensity) sounds and extremely loud (high intensity) sounds.