What does an increase of +3 dB represent in terms of power?

An increase of +3 dB represents a doubling of power. The decibel (dB) scale is logarithmic, meaning that every increase of approximately 3 dB corresponds to a doubling of the power. This is derived from the formula that relates decibels to power:

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

where (P_2) is the new power level and (P_1) is the reference power level. When you calculate the difference in decibels for a doubling of power:

[ 3 , \text{dB} = 10 \log_{10} (2) ]

This relationship indicates that an increase of +3 dB means that the power has increased to twice its original amount. Understanding this relationship is essential for interpreting changes in sound intensity, especially in fields such as acoustics, audio engineering, and hearing sciences. The other options do not accurately represent this fundamental aspect of the dB scale.