Convert amplitude ratio to decibels (dB): if the amplitude ratio (output/input) is 0.1 for a sinusoidal steady-state signal, compute the corresponding value in decibels using 20*log10(AR).

Introduction / Context:
In frequency-response analysis and instrumentation, gains are often expressed on a decibel scale for convenient visualization over many orders of magnitude. Converting amplitude ratio (AR) to decibels (dB) uses a logarithmic formula tied to power ratios and sinusoidal magnitudes.

Given Data / Assumptions:

• Amplitude ratio AR = 0.1 (i.e., output is one-tenth of input).
• Decibel conversion for magnitudes is dB = 20 * log10(AR).
• Base-10 logarithms are used.

Concept / Approach:
Because power is proportional to magnitude squared, the factor “20” appears for converting magnitude ratios, while “10” is used for power ratios. Thus, to convert AR to dB, multiply 20 by the common logarithm of the ratio.

Step-by-Step Solution:

Verification / Alternative check:
As a quick mental check, −6 dB roughly halves amplitude; −20 dB corresponds to 0.1 amplitude, consistent with the logarithmic scale.

Why Other Options Are Wrong:

Common Pitfalls:
Using 10*log10 for magnitude ratios (that is for power), or mixing natural logs with base-10 logs without conversion.

Final Answer:
-20