What is the change in decibels when the output of an audio amplifier is decreased from 75 watts to 50 watts?

To determine the change in decibels when the output of an audio amplifier decreases from 75 watts to 50 watts, we can use the formula for calculating decibel change based on power levels. The formula is:

[ \Delta dB = 10 \times \log_{10} \left( \frac{P_2}{P_1} \right) ]

Where ( P_1 ) is the initial power (75 watts) and ( P_2 ) is the final power (50 watts).

First, we calculate the ratio of the two power levels:

[ \frac{P_2}{P_1} = \frac{50}{75} = \frac{2}{3} \approx 0.6667 ]

Next, we apply this ratio to the decibel formula:

[ \Delta dB = 10 \times \log_{10} (0.6667) ]

Using logarithmic tables or a calculator to evaluate ( \log_{10} (0.6667) ), we find that:

[ \log_{10} (0.6667) \approx -0.1761 ]

Now, substituting this value into the equation gives