How does sound decay with distance ?

The way sound changes with distance from the source is dependent on the
size and shape of the source and also the surrounding environment and
prevailing air currents. It is relatively simple to calculate provided
the source is small and outdoors, but indoor calculations (in a
reverberant field) are rather more complex.

If the noise source is outdoors and its dimensions are small compared
with the distance to the monitoring position (ideally a point source),
then as the sound energy is radiated it will spread over an area which
is proportional to the square of the distance. This is an ‘inverse
square law’ where the sound level will decline by 6dB for each doubling
of distance.

Line noise sources such as a long line of moving traffic will radiate
noise in cylindrical pattern, so that the area covered by the sound
energy spread is directly proportional to the distance and the sound
will decline by 3dB per doubling of distance.

Close to a source (the near field) the change in SPL will not follow
the above laws because the spread of energy is less, and smaller
changes of sound level with distance should be expected.

In addition it is always necessary to take into account attenuation due
to the absorption of sound by the air, which may be substantial at
higher frequencies. For ultrasound, air absorption may well be the
dominant factor in the reduction.