Since `W_0=10^(-12)\ "W/m"^2`, and using the logarithm law for the log of a fraction, we can write:
`P=10\ log\ (W)/(10^-12)`
`=10(log\ W-log\ 10^(-12))`
Now, using the formula for the derivative of a logarithm, and because log 10-12 is a constant, we have:
Now we substitute our given values for W and `(dW)/dt` from the question:
The units are dB/s since the sound pressure (in dB) is changing over time.
Please support IntMath!