Sound Intensity decreased by 75% is how decibels of attenuation?

• A. 6dB
• B. 9 dB
• C. 5 dB
• D. 10 dB

Answer: (A)

Decibels quantify a ratio of intensities on a logarithmic scale, so a percentage change in intensity translates to a specific dB value through the formula dB = -10 log10(I2/I1). If the intensity drops to 25% of its original value, I2/I1 = 0.25. Plugging in gives -10 log10(0.25) = 10 log10(4) ≈ 10 × 0.60206 ≈ 6.02 dB. So the attenuation is about 6 dB.

This matches because a fourfold decrease in intensity corresponds to roughly 6 dB. A larger dB value (like 9 or 10) would indicate a stronger reduction (closer to 12.5% or 10% of the original), and a smaller value (like 5 dB) would correspond to a less than fourfold reduction.