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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Step 2:: Understand the Decibel (dB) Scale
L_{f} = 10 \log_{10}\left(\frac{f}{f_{0}}\right)
The decibel scale is a logarithmic unit used to express the ratio of two values. The formula for converting frequency to decibels is:
Step 3:: Identify the Given Frequency
We have $$f = 20 \mathrm{~Hz}
The reference frequency f_{0} = 1 \mathrm{~Hz}
Step 4:: Calculate the Decibel Value
L_{f} = 13.0103 \mathrm{~dB}
Substitute the values into the formula:
Final Answer
20 \mathrm{~Hz} = 13.0103 \mathrm{~dB}
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