Gracey & Associates

Noise and Vibration Measurement Basics

The decibel - dB

The decibel (abbreviated dB) confuses many people, perhaps because they assume it is an absolute unit or level of sound.

The decibel is not a unit in the sense that a millimetre or a kilogram are well-defined units of distance and weight - you can even see the British Standard metre and kilogram at the NPL if you want to. A decibel, on the other hand, is a relationship or ratio between two sound levels.

Why use decibels, why not stick to the real units that are directly measurable? Hopefully the reason will be clear when we understand how sensitive the human ear is.

The smallest sound we can hear has a power level of about 0.000000000001 watt/sq. metre and the threshold of pain is around 1 watt/sq. metre, which is a range of a million million to 1. So how do you describe these levels and the stages between in meaningful numbers.

Enter Alexander Graham Bell, the Scottish telephone engineer, who suggested simply converting these enormous numbers into logarithms so the threshold of hearing would be 0 and the threshold of pain would be 12 and call them Bels. This was adopted for a while, but it was soon found that compressing such a wide range down to 12 was going too far the other way, it was therefore decided to multiply the answer by 10 and call them decibels i.e. 1 bel = 10 decibels. This meant the range would be from 0 to 120 dB, with 120 steps in between, much more sensible.

How does that work out in the real world? If we put 10 identical noise sources in a room, then there is 10 times as much energy so the measured sound level increases by 10 dB, which is quite logical. Similarly if we had doubled the power i.e. two machines, then the measured increase would only be 3 dB.

In the first case we had 10 times as much power and the log of 10 is 1 bel or 10 dB. Similarly twice as much power or a factor of 2 gives a log of 0.3 bels or 3 dB.

It follows therefore that if one machine = 90 dB, then 2 = 93 dB and 10 machines = 100 dB. If you then doubled the number of sources from 10 to 20 the measured level would only increase by a further 3 dB to 103 dB.

You would need to cram 100 machines into the room to increase the level to 110 dB or a 1000 machines to measure 120 dB, which is the threshold of pain for most people.

Conversely if you switched off one machine in a room containing 100 machines you would never notice because you would have to switch off 50 before the level came down by 3 dB.

If 1 = 90 dB : 2 = 93 dB : 10 = 100 dB : 20 = 103 dB : 50 = 107 dB : 100 = 110 dB