Antoine LAURENT General Engineer holding a state degree and an ENSAM graduate of June 2003. 3rd year training in Acoustic Vibration and Sound Wave Propagation. Assignments in acoustics for FFBT and FFT for more than 10 years. More than 120 cases handled. Permanent member for the past 10 years of the S30J commission (environmental noise) at AFNOR. Standard S31-010. Member of the "shooting range noise" WG for drafting FD S31-160. Which became a fully-fledged standard in 2019. Member since 2019 of the new S30E Commission (S30J and S30M merged). Member representing France and AFNOR at the commission: WG 51 (noise emission from shooting ranges). As part of ISO/TC 43 Clarifications on the logarithmic decibel scale in acoustics The decibel is the unit used to express noise intensity. Its origin and how it functions are somewhat special compared to the other scales of units. Noise is vibrating air, i.e. a rapid change in air pressure. These variations in sound pressure are picked up by the eardrums, and the intensity at which the eardrums vibrate is transmitted to the brain, which interprets it as a sound, a note, or a specific noise. The human ear is sensitive to noise at sound pressures ranging from 0.00002 Pa to 200 Pa (atmospheric pressure is 101,300 Pa (Pa stands for pascal, the unit of pressure). Two facts arise from these figures: • The pressure picked up by the ears is extremely weak compared to atmospheric pressure (about one ten-billionths); • The range between soft and loud sounds stretches a very long way on the pressure scale: from a very small number (0.00002) to a very large number (200). This second point makes noise level notation impractical: one would have to deal with far too many figures in calculations or legislation relating to noise pollution. Furthermore, it was discovered (in 1860) that a sound with an acoustic pressure of 1.5 Pa will be as loud compared to a sound of 1 Pa, as another sound of 0.015 Pa is compared to a sound of 0.01 Pa, even though the pressure is increased by 0.5 Pa in one case, and by only 0.005 Pa in the other. Therefore, it is not the absolute sound pressure variation that matters, but the relative difference between two sounds (50% here). 1 / 2 As a result, a decision was made to use a scale for sound that accounts for relative rather than absolute variations between two values: a logarithmic scale, in decibels. This way of measuring sound also has the property of reducing the range of the scale: instead of going from 0.01 to 100,000, it will go from -2 to +5, which is much more convenient. However, the use of the decibel introduces a problem: it is one of the only instances in everyday life when a logarithmic and therefore non-linear scale is used. This can be confusing in practice. For instance, if a machine emits 40 dB of noise, how many decibels will four of these machines produce? Answer: 46 dB, and not 160! As another example, if an installation emits 40 dB, how many of these installations are needed to produce 160 dB of noise? Answer: 1,099,511,627,776, and not 4! In fact, the logarithmic scale works like this: • adding 3 dB means multiplying the sound intensity by two: 26 dB is therefore twice as loud as 23 dB and 23 dB is in turn twice as loud as 20 dB. • subtracting 3 dB means dividing the sound intensity by two. So, if you increase the sound level by 12 dB, you multiply the sound intensity by sixteen! Calculation details: So in our case, if we compare steel ball ammunition and lead shot ammunition, a difference of 6 dB(A) on exit actually represents a noise level perceived by the ears multiplied by 4! Antoine LAURENT 2 / 2 .