Doubling the distance from a sound source results in a decibel change of

Doubling the distance from a sound source results in a decibel change of

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

Answer: (D)

When sound spreads in a free field from a point source, the energy disperses over a larger area, so intensity falls off with the square of the distance (I ∝ 1/r^2) and the pressure falls roughly as p ∝ 1/r. Decibels measure a log ratio, so doubling the distance makes the pressure half as large: ΔL = 20 log10(1/2) ≈ -6.02 dB. The same rule applies to intensity, giving ΔL ≈ -6 dB. So, doubling the distance reduces the sound level by about 6 dB, assuming no absorption or reflections.

When sound spreads in a free field from a point source, the energy disperses over a larger area, so intensity falls off with the square of the distance (I ∝ 1/r^2) and the pressure falls roughly as p ∝ 1/r. Decibels measure a log ratio, so doubling the distance makes the pressure half as large: ΔL = 20 log10(1/2) ≈ -6.02 dB. The same rule applies to intensity, giving ΔL ≈ -6 dB. So, doubling the distance reduces the sound level by about 6 dB, assuming no absorption or reflections.