A single Formula 1 car passing by makes a noise of around 110 decibels. Last year I went to a Formula 1 Grand Prix and sat near the start line, where 20 cars left the grid at once. The noise was mind-numbing, much louder than a single car, but not 20 times louder (or 2200 decibels, an unachievable figure). Why wasn鈥檛 it?
鈥� There are two things here. First, the sound sources are not synchronised: the cars are making noise independently of one another, and so a burst of loud noise from one might coincide with a drop in noise from another. For these unsynchronised sound sources, the sound pressure (the air compressions that your ear detects) increases only according to the square root of the number of sources.
Second, the decibel (dB) scale is logarithmic: things don鈥檛 just add together neatly. The increase in the decibel level is the logarithm of the ratio of the number of sources (in this example, 20/1) multiplied by 10. The 19 extra cars add only around 13 dB, so the noise from 20 cars will be just 123 dB or thereabouts.
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鈥淭he decibel scale is logarithmic, so things don鈥檛 just add together: 19 extra cars only add about 13 dB鈥�
The same is true for violins in an orchestra. The 16 violins in an orchestra produce only four times as much volume as a single violin: if one violin produces 70 dB, 16 produce 82 dB. Similarly, silencing half of the trumpets 鈥� which are obviously much louder than violins 鈥� only reduces their volume by a few decibels, which explains why you need so many more violins than trumpets in an orchestra.
This also has implications for traffic-noise control. If the noise emanating from a car engine is roughly the same level as the noise from its tyres then there鈥檚 not much point in reducing engine noise by more than about 3 dB without also reducing the tyre noise.
Hugh Hunt, University of Cambridge, UK
鈥� Back in 1990, I measured sound levels at a Grand Prix at Silverstone in the UK for health and safety. I found that the sound level from a single car passing, measured in the pits, was indeed about 110 dB.
The sound level varied widely throughout the race. In the first lap, all the cars passed by my measuring point virtually at once, but at the end all the cars were well spread out around the track. The difference in maximum level between the first lap and later laps where the cars were spread out was variable but around 12 dB, close to what theory predicts.
Loudness to a human observer is another matter altogether and differs from recorded sound levels. The human ear works using ratios, so doubling the sound power always produces roughly the same increase in loudness, no matter where you start.
A rule of thumb that works pretty well for most people is that an increase of 10 dB corresponds to 鈥渢wice as loud鈥�, so 20 cars passing at once would be a bit more than twice as loud as one car to a listener such as your questioner 鈥� the 13 dB given by the first correspondent.
This just goes to prove that the decibel is a very confusing unit of measurement. With this in mind I鈥檝e taken on the challenge of explaining decibels for people who don鈥檛 know what a logarithm is, at .
鈥淭he answers to this question show that the decibel is a very confusing unit of measurement鈥�
Tony Woolf, Acoustic consultant, London, UK