If an audio amplifier’s power decreases from 20 watts to 9 watts, what is the expected change in decibels?

To determine the change in decibels when an audio amplifier's power decreases from 20 watts to 9 watts, the formula used involves the logarithmic relationship between power levels and decibels:

[

\Delta dB = 10 \log_{10}\left(\frac{P2}{P1}\right)

]

In this scenario:

• (P1) (initial power) is 20 watts.

• (P2) (final power) is 9 watts.

Substituting these values into the formula gives:

[

\Delta dB = 10 \log_{10}\left(\frac{9}{20}\right)

]

Calculating the fraction:

[

\frac{9}{20} = 0.45

]

Next, computing the logarithm:

[

\log_{10}(0.45) \approx -0.34657

]

Now, multiplying by 10:

[

\Delta dB \approx 10 \times -0.34657 \approx -3.4657 \text{ dB}

]

Rounding this value gives approximately -3.5 dB.

This indicates that a decrease in power from 20