If the sound pressure level is stated in dB, this information can be used in calculations. Expressed in dB: 20 x log (0.1 / 1) = -20 dB.Įxample 3: The attenuator (example 2) is connected to the output of the amplifi er (example 1). The ratio between output and input is 0.1/1 = 0.1. The gain is thus 1000-fold (1000: 1), or 20 x log (1,000 / 1) = +60 dB.Įxample 2: An attenuator attenuates a voltage to one-tenth. The following table shows a few relationships governing the calculation of physical values and decibel values, and the conversion between these types of values:Įxample 1: An amplifier amplifies an input signal of 1 mV (millivolts) to an output signal of 1,000 mV. Nowadays, however, it has become common to omit the ‘SPL’ when discussing sound pressure levels. Because there is a defined reference value, in this case ‘SPL’ is appended to the unit ‘dB’. In the case of sound pressure ratios, the auditory threshold is used, having a value of 20 μPa. Sound pressure, voltage or current ratios in dB: 20 x log 10 (value/reference value) Power ratio in dB: 10 x log 10 (power/reference power) or 10 x log 10 (P/P 0) For sound pressures, voltages and currents, the factor is 20. The result is the Bel, one-tenth of which is one deci-bel, i.e. We use the logarithm to base 10, which is generally given as ‘log’ on calculator keypads. The general calculation is as follows: log (value/reference value). As well, the gigantic ratio of barely perceptible sound pressure (the auditory threshold) to the loudest tolerable sound pressure (pain threshold) of 1: 3,000,000 is compressed into a much more manageable scale of 0 to 130 dB. Using a logarithmic scale is a much better approximation of human hearing than the linear variables. Meaning of and computations using decibelsĪ decibel (dB) represents the ratio of two variables on a logarithmic scale, and has no base unit (e.g.
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