Question 632961: Find the number of decibels for the power of the sound. Round to the nearest decibel.
A rock concert, 5.37 10^-6 watts/cm2
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! first table converts dbm to milliwatts
http://www.rapidtables.com/convert/power/dBm_to_mW.htm
second table converts milliwatts to dbm
http://www.rapidtables.com/convert/power/mW_to_dBm.htm
third tabletable converts watts to dbm
http://www.rapidtables.com/convert/power/Watt_to_dBm.htm
based on the third table, you would enter .00000537 as the power in watts and it will tell you that the power in decibels is equal to -22.700257143.
based on the first table, you would enter -22.700257143 as the power in decibels and it will tell you that the power in milli-watts is equal to 0.00537.
based on the second table, you would enter .00537 as the power in milli-watts and it will tell you that the power in decibels is equal to -22.700257143.
these calculators take the burden of converting from decibels to milli-watts and vice-versa.
the theory involves logarithms.
the basic formula is:
y = log(x) if and only if x = 10^y
if y is in decibels, then the formula becomes:
y = 10*log(x) if and only if x = 10^(y/10)
this assumes x is in milli-watts
if x is in watts, then this equation becomes:
y = 10*log(1000*x) if and only if 1000*x = 10^(y/10)
this can be further simplified to:
y = 10*log(1000*x) if and only if x = (10^(y/10))/1000
note that if x is in milliwatts, then x is equal to .00537 (5.37*10^-3)
note that if x is in watts, then x is equal to .00000537 (5.37*10^-6)
note that 1000 * .00000537 is equal to .00537 (5.37*10^-6*10^3 = 5.37*10^-3)
the conversions are tricky, but they work.
the basic power reference in milliwatts is 0 dbmw = 1 milliwatt of power.
the basic power reference in watts is 0 dbw = .001 watt of power.
1000 milliwatts equals 1 watt
.001 watts equals 1 milliwatt
this is about as simple as i can make it.
those tables are a godsend.
they take the drudgery out of doing the conversions.
the theory is interesting but can get complex.
use the tables unless you have to do it manually.
the tables have the conversion formulas you can use if you have to do it manually.
some more information regarding decibels can be found here:
http://en.wikipedia.org/wiki/Decibel
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