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For less trivial cases, online calculators are available.Ĭaution: All of the above assumes decibels are used to express ratios of field quantities.You might have seen this as the “mute” position on some volume knobs. This might seem strange, but this property makes decibels very convenient to use in practice - it’s easier to add than to multiply. When combining ratios, decibels don’t multiply they add up.To invert the ratio, just change the sign: for example, -6 dB is the same as dividing by 2.The most useful ratios to keep in mind are +6 dB (×2) and +20 dB (×10).The trick is to not fight their logarithmic nature, but embrace it. This will be clearer with examples: Amplitude ratioīecause the decibel is a logarithmic unit, it behaves differently from more conventional linear units. What sets the decibel apart is that it is also a logarithmic unit, meaning that its value is proportional to the logarithm of the ratio, not the ratio itself. The decibel (dB) is, in its purest form, a dimensionless unit that represents a ratio between two quantities, just like “×” or “%”. Now, if only there was a unit that made working with ratios easier… Enter the decibel This is very convenient because it means that a given ratio (often called gain) has the same meaning regardless of context. This means that a given ratio applies in all three domains: twice the sample value is also twice the voltage and twice the sound pressure. Remember that all three quantities (sample value, voltage, and sound pressure) are proportional to each other when the audio signal moves from one realm to the next. There is another advantage to using ratios.
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This makes a compelling case for using ratios, not differences, when comparing amplitudes. However, the ratio is very different in the former case it’s ×2, in the latter case it’s ×1.1. In both cases the absolute difference is the same: 0.1 Pa. The difference in loudness between 1.0 Pa and 1.1 Pa is barely noticeable.The difference in loudness between 0.1 Pa and 0.2 Pa is very noticeable.In audio, we care more about ratios of quantities (e.g. There are good reasons for this, and they have to do with how we humans perceive loudness. Instead, one often finds such quantities expressed in decibels (dB) or a related unit. However, in the audio literature, marketing materials and equipment specifications, these are not the units that are typically used. In the acoustic domain, it is a pressure difference in pascals (Pa).In the analog domain, it is voltage in volts (V).In the digital domain, it is a sample value.In the previous post, I introduced a number of physical quantities that are used to describe the amplitude of an audio signal: