The formula to calculate the dB per decade is:
\[ \text{dB/Decade} = \frac{\text{Final Level} - \text{Initial Level}}{\log_{10}(\frac{\text{Final Frequency}}{\text{Initial Frequency}})} \]
Where:
dB per decade is a measure of how much the level of a signal or sound changes over a tenfold increase in frequency. It is commonly used in audio engineering, electronics, and acoustics to describe the behavior of filters, amplifiers, and other frequency-dependent systems. A positive dB per decade indicates an increase in level with frequency, while a negative value indicates a decrease.
For example, if the initial frequency is 100 Hz, the final frequency is 1000 Hz, the initial level is 20 dB, and the final level is 40 dB, the dB per decade can be calculated as follows:
\[ \text{dB/Decade} = \frac{40 - 20}{\log_{10}(\frac{1000}{100})} = \frac{20}{\log_{10}(10)} = \frac{20}{1} = 20 \]
So, the dB per decade for these values is 20.