Ask Me Help Desk - Physics:Intensity

17.Two sources have sound levels of 75 dB and 80 dB. If they are sounding simultaneously, what is the combined sound level ?

Ans:81.2 db

How am I supposed to this? What is the formula.I really don't know.Can someone show me the solution.The given answer is 81.2 db.Thanks

Since dB's are a logarithmic scale, you can't add them directly. It's easiest to convert from dB into W/m^2, add the two intensities, and then convert back into dB.

To go from W/m^2 to dB, the formula is:

$L_I=10 \cdot \log (\frac {I}{I_{ref}})$ ,

where $L_I$ is the intensity in dB, $I$ is the intensity in W/m^2, and $I_{ref}$ is the reference intensity (which is equal to $10^{-12}$ W/m^2 by definition.

So can you solve the above formula for $I$ so you can calculate the intensity in W/m^2? Just do it for both sources, then do as I said and add them together, then convert back to dB with the above formula.

Remember, it's log base 10, so to "undo" the log when solving the equation for I, you need to raise 10 to the power of each side of the equation.