It is desired to raise the power to a speaker from 15 W to 30 W. This is a:

It is desired to raise the power to a speaker from 15 W to 30 W. This is a:

• A. 1 dB increase
• B. 5 dB increase
• C. 3 dB increase
• D. 10 dB increase

Answer: (C)

To determine the increase in power needed to raise the output from 15 W to 30 W, the relevant formula involves the decibel (dB) scale, which is logarithmic in nature. The general formula for calculating the change in decibels based on power is: \[ \Delta dB = 10 \cdot \log_{10}\left(\frac{P_2}{P_1}\right) \] Where \(P_2\) is the final power of 30 W and \(P_1\) is the initial power of 15 W. Plugging in the values gives: \[ \Delta dB = 10 \cdot \log_{10}\left(\frac{30}{15}\right) = 10 \cdot \log_{10}(2) \] The logarithm of 2 is approximately 0.301, therefore: \[ \Delta dB \approx 10 \cdot 0.301 = 3.01 \, dB \] This value rounds to approximately 3 dB. An increase of 3 dB indicates that the power level has effectively doubled (in this case, from 15 W to 30 W), which

To determine the increase in power needed to raise the output from 15 W to 30 W, the relevant formula involves the decibel (dB) scale, which is logarithmic in nature. The general formula for calculating the change in decibels based on power is:

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

Where (P_2) is the final power of 30 W and (P_1) is the initial power of 15 W. Plugging in the values gives:

[ \Delta dB = 10 \cdot \log_{10}\left(\frac{30}{15}\right) = 10 \cdot \log_{10}(2) ]

The logarithm of 2 is approximately 0.301, therefore:

[ \Delta dB \approx 10 \cdot 0.301 = 3.01 , dB ]

This value rounds to approximately 3 dB.

An increase of 3 dB indicates that the power level has effectively doubled (in this case, from 15 W to 30 W), which