in the formuls B(decibel)=10log_10(I/I_0) I is sound intensity in units of watts per meter squared (W/m2). I_0 is constant, at 10^−12 W/m2?
Update:
βis also sound intensity, but measured in dimensionless units called decibels.
Find dβ/ dI when I = 10−3 W/m2.
and
Find dβ /dI when β = 95 decibels.
please show work this is the only hw question I don't understand
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Answers & Comments
No no no. Stare at B = 10 log(I/I0); this is just a ratio multiplied by 10, which is unitless. And what units do ratios have?
They don't. They are also unitless because in ratios both the numerator and the denominator are the same units and like variables, units divided. So the units above are divided by the same units below, and that yields 1. You know, like W/m^2//W/m^2 = 1.
Decibels are defined units. And their definition is (duh) B = 10 log(I/I0)
We see this in physics a lot. You've heard of G's? As in how many G's does the pilot pull in turning in his jet?
Well that's a ratio G = A/g where A is the acceleration in a turn and g is the acceleration due to gravity. But as both accelerations are m/s^2 in one SI set of units, the ratio G = A/g is actually unitless. But we define that specific ratio as G's.
Just like we define B = 10 log(I/I0) to be decibels.