When the intensity is reduced to 1/10 of its original value, the relative change is:

When the intensity is reduced to 1/10 of its original value, the relative change is:

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

Answer: (B)

Decibels quantify how a power or intensity quantity changes on a logarithmic scale. For intensity, the relative change is given by dB = 10 log10(I2/I1). If the intensity drops to one tenth of its original value, I2/I1 = 0.1. Since log10(0.1) = -1, the calculation is 10 × (-1) = -10 dB. So the relative change is -10 dB, meaning the intensity is reduced by a factor of ten. (If you were discussing amplitude instead of intensity, the result would differ—about -20 dB for a tenfold drop—because amplitude relates to power by squaring.) The other options correspond to different ratios: about a half for -3 dB, about a doubling for +3 dB, and a tenfold increase for +10 dB.

Decibels quantify how a power or intensity quantity changes on a logarithmic scale. For intensity, the relative change is given by dB = 10 log10(I2/I1). If the intensity drops to one tenth of its original value, I2/I1 = 0.1. Since log10(0.1) = -1, the calculation is 10 × (-1) = -10 dB. So the relative change is -10 dB, meaning the intensity is reduced by a factor of ten. (If you were discussing amplitude instead of intensity, the result would differ—about -20 dB for a tenfold drop—because amplitude relates to power by squaring.) The other options correspond to different ratios: about a half for -3 dB, about a doubling for +3 dB, and a tenfold increase for +10 dB.