How does the decibel change when you double the distance?

How does the decibel change when you double the distance?

• A. Increases by 6 dB
• B. Decreases by 6 dB
• C. Decreases by 3 dB
• D. Increases by 3 dB

Answer: (B)

When you move away from a point source, the sound energy spreads over a larger area, so the intensity drops with the square of the distance (inverse-square law). Doubling the distance makes the intensity become one quarter of the original. In decibels, the change is 10 log10(I2/I1) = 10 log10(1/4) ≈ -6.0 dB. Since sound pressure falls off as 1/r in a free field, the SPL also decreases by 20 log10(1/2) = -6.0 dB. So the sound level decreases by about 6 dB when distance is doubled. The other options imply an increase or a smaller decrease, which don’t match this physical behavior.

When you move away from a point source, the sound energy spreads over a larger area, so the intensity drops with the square of the distance (inverse-square law). Doubling the distance makes the intensity become one quarter of the original. In decibels, the change is 10 log10(I2/I1) = 10 log10(1/4) ≈ -6.0 dB. Since sound pressure falls off as 1/r in a free field, the SPL also decreases by 20 log10(1/2) = -6.0 dB. So the sound level decreases by about 6 dB when distance is doubled. The other options imply an increase or a smaller decrease, which don’t match this physical behavior.