In acoustics and audio engineering, decibels (dB) are used to express the ratio of two quantities, such as sound pressure levels or amplitudes. The decibel scale is logarithmic, which means that a change of 10 dB corresponds to a tenfold change in the quantity being measured.
To determine the amplitude corresponding to a specific decibel value, we need a reference value. In acoustics, the commonly used reference value is 20 microPascals (μPa), which represents the threshold of human hearing.
In the case of sound pressure level, the formula to convert from decibels to the corresponding pressure ratio is:
Pressure Ratio = 10^(dB/20)
To convert from the pressure ratio to the corresponding amplitude, we use the equation:
Amplitude = Pressure Ratio * Reference Amplitude
For sound pressure levels, the reference amplitude is typically taken as the RMS (Root Mean Square) value of the reference pressure, which in this case is 20 μPa.
Therefore, to find the amplitude corresponding to 20 dB, we can calculate as follows:
Pressure Ratio = 10^(20/20) = 10^1 = 10
Amplitude = Pressure Ratio * Reference Amplitude = 10 * 20 μPa = 200 μPa
So, the amplitude corresponding to 20 dB is 200 microPascals (μPa).