What is the characteristic sound pressure change when the distance is tripled, assuming all other factors remain constant?

When analyzing sound pressure levels in relation to distance, it's essential to understand the inverse square law, which states that sound intensity decreases as the square of the distance from the source increases. Specifically, if the distance from a sound source is tripled, the intensity of the sound will decrease by a factor of nine.

To find the change in sound pressure level in decibels (dB), we can apply the formula:

[ \text{Change in dB} = 10 \times \log_{10}\left(\frac{I_1}{I_2}\right) ]

Since intensity is proportional to the square of the sound pressure (P), we can relate changes in sound pressure level to changes in distance. Tripling the distance results in a decrease in intensity by a factor of nine, which translates to:

[ 10 \times \log_{10}(9) \approx 10 \times 0.954 = 9.54 \text{ dB} ]

This change in intensity corresponds to a decrease in sound pressure level of approximately 9.54 dB.

However, in dealing with sound pressure, the change is actually half this value because sound pressure levels are measured in a way that accounts