Measured Sound in a Room

If the sound field in a room followed the inverse square law, then each doubling of distance from the source would give a drop of 6 decibels. The descending straight line on the plot at right represents inverse square law behavior, but you can see that the measured sound does not behave like that except in a narrow distance range.

Notes on Room Sound Measurement

Measurements in a laboratory room. Enclosed 6x9 inch speaker, white noise. # d(cm) dB dBA 1 2 90 90 2 4 89.6 89.4 3 8 88.8 88.8 4 16 87.1 87.7 5 32 86 85.4 6 64 81.5 80.6 7 128 77 76.4 8 256 72.2 71.6 9 512 68.8 68.3 The measurements in decibels and dBA were very similar, indicating that the room was fairly free of low frequency, inaudible sounds.

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Effect of Doubling Distance

If the inverse square law applies, then doubling the distance from a point sound source will cause the intensity to drop by 6 decibels. The intensity difference in decibels between two sounds A and B is given by

If sound B is measured at double the distance of sound A from a point source so that it follows the inverse square law, then its intensity will be one fourth that of A. The difference in decibels is then

In a real room, reverberation will contribute to the sound field so that the sound will not drop off as rapidly as the inverse square law predicts.