By doubling the distance from a sound source, how much will the sound pressure level decrease?

Doubling the distance from a sound source results in a decrease in sound pressure level due to the inverse square law, which states that sound intensity decreases with the square of the distance from the source. When you double the distance, the intensity of the sound decreases to one-fourth of its original value.

Sound pressure level (SPL) in decibels is calculated using a logarithmic scale, specifically with a reference intensity. When intensity is reduced to one-fourth, the corresponding change in decibels is a decrease of 6 dB. This relationship is derived from the formula for calculating decibels: a change in intensity by a factor can be quantified as:

[ L = 10 \times \log_{10}(I/I_0), ]

where I is the intensity and ( I_0 ) is a reference intensity.

Since intensity decreases by a factor of 4 when distance is doubled, the change in level can be calculated as:

[ 10 \times \log_{10}(1/4) = 10 \times \log_{10}(10^{-2}) = -20 , dB. ]

However, when calculating the decrease due to changes in distance, the decrease is often