![]() ![]() I hope these are enough and satisfactory. Optical loss is measured in dB which is a relative measurement. Where \$p\$ is the sound pressure level (SPL) and \$z_0\$ is the specific acoustic impedance (think of it as something like a characteristic impedance). Sound power ( \$P\$) is proportional to the sound intensity ( \$I\$):Īnd sound intensity ( \$I\$) is proportional to the square of sound pressure: I imagine power is proportional to the square of pressure but I can't figure out where, when it comes to sound waves. So for something like voltage, where \$P = V^2/R\$, you have \$dB= 10 \log((V^2/R) / (V_0^2/R)) = 10 \log((V/V_0)^2) = 20 \log(V/V_0)\$ so I understand that if you have some squared quantity in there you can pull out the exponent of 2 in the log function and that gets you the multiplier of 2 on the outside, hence the 10 becoming 20 in the case of voltage rather than power.īut in the sound equation I can't derive the origin of the 20 by somehow relating power to pressure. \$dB = 10 \log(P / P_0)\$ for measured power \$P\$ and reference power \$P_0\$. Now that you understand the basic formula used for calculating ratios in Bels, let’s see how we adjust that formula to calculate ratios in decibels. ![]() I know that the 10 comes from the equation when relating quantities of power: Where \$p_s\$ is the pressure of the measured sound wave (in Pascals) and \$p_0\$ is some fixed reference pressure.īut where does the 20 come from in this particular equation? For sound levels, it is said that decibels follow this equation: ![]()
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