MadSci Network: Physics

Re: Is it possible to convert decibel to watts and joules?

Date: Mon Apr 13 07:24:01 2009
Posted By: Tetjana Ross, Faculty, Oceanography, Dalhousie University
Area of science: Physics
ID: 1238486132.Ph

Hi Yao Zhi,

1.) Is it possible to convert decibel to watts?
You really need to know the definition of your particular decibel in order to answer this. Decibels, being a logarithmic scale, should really be dimensionless, but occasionally they are dimensional. In acoustics decibels are often defined as 10 times the log-base-ten of the ratio of the acoustic power to a reference power see Wikipedia . Then if you know the reference power, conversion to watts is straightforward. (If x is the decibel value, then P_x=P_0*10^(x/10) watts.) Sometimes, however, decibels are defined differently, as either 10 times the log-base-ten of the scattering cross-section (as in Target Strength, dB re m^2) or 10 times the log-base-ten of the scattering cross-section per unit volume (as in Volume Scattering Strength, dB re m-1). So there isn't a clear answer to your question, you really need to know what kind of dB you're trying to convert.

2.) Is it possible to convert decibel to joules?
Again, this depends on what kind of decibels. Assuming the former example, with P_x=P_0*10^(x/10) watts of power, then given an appropriate time, T, (e.g. the duration of the emitted sound pulse), you could calculate P_x * T joules.

3.) Is it possible to create a billion decibel?
Again, it depends. For the scattering cross-section examples, the answer is no. For the relative power example, I suppose you could just choose an unrealistically small P_0 such that the relative dB = 1 billion.

4.) What can a billion decibel do?
No idea. This depends entirely on your definition of dB. Using a realistic reference power (P_0), a billion dB could not be achieved. We're talking about a logarithmic scale here. If x=10^9 dB, P_x=10^100000000 * P_0. If P_0 is unrealistically small, however, a billion dB might be a pleasant sound level.

I hope this helps.

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