When the intensity is reduced to 1/2 its original value the relative change is ______.

When the intensity is reduced to 1/2 its original value the relative change is ______.

• A. -1dB
• B. -3dB
• C. -0dB
• D. -6dB

Answer: (B)

When we measure how much a power level changes in decibels, we use the power form of the decibel equation: dB change = 10 log10(P2/P1). Halving the intensity means P2/P1 = 1/2. So the change is 10 log10(1/2) = 10 × (-log10 2) ≈ -3.01 dB, which is commonly rounded to -3 dB. This is the standard reference that a -3 dB change corresponds to a reduction by half the power. The other values would correspond to different power ratios: about -1 dB is a smaller drop (roughly 0.79 of the original), 0 dB means no change, and -6 dB corresponds to a quarter of the original power.

When we measure how much a power level changes in decibels, we use the power form of the decibel equation: dB change = 10 log10(P2/P1). Halving the intensity means P2/P1 = 1/2. So the change is 10 log10(1/2) = 10 × (-log10 2) ≈ -3.01 dB, which is commonly rounded to -3 dB. This is the standard reference that a -3 dB change corresponds to a reduction by half the power. The other values would correspond to different power ratios: about -1 dB is a smaller drop (roughly 0.79 of the original), 0 dB means no change, and -6 dB corresponds to a quarter of the original power.