If the power of a sound wave is increased by a factor of 8, how many decibels is this?

• A. 8 dB
• B. 3 dB
• C. 9 dB
• D. 6 dB

Answer: (C)

Decibels express power ratios with the formula dB = 10 log10(P2/P1). An eightfold power increase means P2/P1 = 8. So dB = 10 log10(8) ≈ 10 × 0.903 ≈ 9.0 dB. Rounding gives about 9 dB.

For context, doubling the power is about 3 dB, quadrupling is about 6 dB, and an eightfold increase sits around 9 dB. The other options don’t fit because they correspond to different power ratios: 8 dB ≈ 6.3×, 3 dB is a factor of 2, and 6 dB is a factor of 4.