When the intensity is reduced to half, the relative change is:

When the intensity is reduced to half, the relative change is:

• A. 3 dB
• B. -3 dB
• C. -10 dB
• D. -1 dB

Answer: (B)

Decibels express how much a quantity changes on a logarithmic scale. For intensity, the change is 10 times the log base 10 of the ratio of final to initial intensity. If the intensity is halved, the ratio is 1/2, so the change is 10 log10(1/2) = 10 × (−0.3010) ≈ −3.01 dB. The negative sign indicates a decrease, so the relative change is about −3 dB. This is why halving the intensity corresponds to a −3 dB change. The other options would correspond to different factors (e.g., a larger decrease, a tenfold decrease, or an increase), so −3 dB is the correct description for halving.

Decibels express how much a quantity changes on a logarithmic scale. For intensity, the change is 10 times the log base 10 of the ratio of final to initial intensity. If the intensity is halved, the ratio is 1/2, so the change is 10 log10(1/2) = 10 × (−0.3010) ≈ −3.01 dB. The negative sign indicates a decrease, so the relative change is about −3 dB. This is why halving the intensity corresponds to a −3 dB change. The other options would correspond to different factors (e.g., a larger decrease, a tenfold decrease, or an increase), so −3 dB is the correct description for halving.