dB Per Decade Calculator

Calculate dB Per Decade







Formula

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:

What is dB Per Decade?

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.

Example

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.

Extended information about "dB-Per-Decade-Calculator"

10 dB/Decade

Formula: \( \text{Gain (dB)} = 10 \log_{10} \left( \frac{f_2}{f_1} \right) \)

Example: \( \text{Gain (dB)} = 10 \log_{10} \left( \frac{1000}{100} \right) \)

Decades to Years Calculator

Formula: \( \text{Years} = \text{Decades} \times 10 \)

Example: \( \text{Years} = 3 \times 10 \)

dB per Octave to dB per Decade

Formula: \( \text{dB/Decade} = \text{dB/Octave} \times 3.32 \)

Example: \( \text{dB/Decade} = 6 \times 3.32 \)

How to Calculate Decades

Formula: \( \text{Decades} = \frac{\text{Years}}{10} \)

Example: \( \text{Decades} = \frac{50}{10} \)

20 dB/Decade

Formula: \( \text{Gain (dB)} = 20 \log_{10} \left( \frac{f_2}{f_1} \right) \)

Example: \( \text{Gain (dB)} = 20 \log_{10} \left( \frac{2000}{200} \right) \)

40 dB/Decade

Formula: \( \text{Gain (dB)} = 40 \log_{10} \left( \frac{f_2}{f_1} \right) \)

Example: \( \text{Gain (dB)} = 40 \log_{10} \left( \frac{3000}{300} \right) \)

dB per Decade in Octave

Formula: \( \text{dB/Octave} = \frac{\text{dB/Decade}}{3.32} \)

Example: \( \text{dB/Octave} = \frac{30}{3.32} \)

How Many Minutes in a Decade Calculator

Formula: \( \text{Minutes} = \text{Decades} \times 10 \times 365 \times 24 \times 60 \)

Example: \( \text{Minutes} = 1 \times 10 \times 365 \times 24 \times 60 \)

How to Calculate dB

Formula: \( \text{dB} = 10 \log_{10} \left( \frac{P_2}{P_1} \right) \)

Example: \( \text{dB} = 10 \log_{10} \left( \frac{100}{10} \right) \)

How Much is a Decade in Years

Formula: \( \text{Years} = \text{Decades} \times 10 \)

Example: \( \text{Years} = 2 \times 10 \)