Depending on the measurement made and the reference used, the equation is either 10(log(measurement/reference)) or 20(log(measurement'/reference')). The latter case (marked with prime marks) is for where reference' and measurement' are squared quantities (done to eliminate negative instantaneous excursions, and make a quantity that is not tied to time); the former for simple instantaneous sound pressure. Look in Benade (whose work I haven't looked at myself in decades) and see if he even states what reference he is using. If his 'loudness' is referenced to Pascals or N/m^2, then the equation to use should be 10(log(pressure/ref)), so 6dB will be doubling. If he is using Pascals^2, then doubling will be 3dB. In light (where I worked for one of the intervening decades), the terms are irradiance and magnitude, irradiance being the amplitude of light, and magnitude being the square of the irradiance, ie the power in the light. For irradiance, 6dB doubles, for power, 3dB doubles. Why? Because of the square function applied to derive power. In sound, especially in 'pro sound', loudness is equated with the volume of sound, which is a power measurement. If Benade is dealing specifically in amplitude of sound rather than power, his loudness means an entirely different thing altogether: hence my remark about sound pressure and power being more useful terms than loudness (which means everything from the knob setting on the amp to the special change in filter characteristics to adjust for the fletcher munson curve to actual power.) Magnitude is also a very heavilly over-used word, which I tend to try to avoid when talking actual values. As for the math, I don't want to tell you how many times I've messed up addition while guessing right at second derivitives (which I can't do on paper to save my life!) raybro Robin Hufford wrote: >Hello William, > I don't know where I came up with 3 plus 3 plus 3 then plus 1.5 is >required to get 10. A mystery to me, except that the post was done in a >hurry. > So what are you saying? Benande takes the position as does Bernhard >that 6db is a doubling of loudness. Perhaps this is corrected for >perception. What is it? >Regards, Robin Hufford > > >
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