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Question:
How many watts are in a decibel? I read heard this terminology in a song.



Replies:
The decibel is dimensionless. It is the logarithm of a ratio. In terms of power, dB = 10 log(base10) P/Po, where Po is the reference power. It often is referenced to 1 milliwatt (.001 watt). Thus, a power of 1 watt referenced to 1 mw would be 10 X log(1W/.001W) = 10 X log(1000) = 30 dB. Anything that can be expressed as a ratio to a reference can be expressed in dB. As a whimsical example, a dollar is 10 X log(100/1) = 20 DB over a penny! So, there are no watts in a dB. The dB has no dimensions. You can use watts to determine dB. If you have a 1 mW signal and send it through an amplifier that boosts that signal to 5 watts, then we say the amplifier has 10 X log(5W/.001W) = 37 dB gain. If you want to relate dB to watts, you must know the reference power.

gary e myers


Well, the question was probably arising from the tendency to rate speakers in watts, and the fact that there is a "unitfull" decibell - the decibell used to measure sound levels. However, the dB level you will feel from a speaker of a given wattage depends on how close you are to the speaker! And I do not know if there is any real standard relation between the dB level 1 foot from a speaker and the power level, though there could be...

Arthur Smith



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