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The Inverse Distance Law

The image above illustrates the reduction in Sound Pressure Level (SPL) over distance in a typical classroom.
With the 18dB reduction at the rear of the room, the Signal to Noise Ratio (SNR) is negative. Even at only 6m distance, the SNR is 0dB.

Dealing with sound is a little different from other energy forms, so I won't try to get too technical or complicated.
Basically we concern ourselves with two aspects of sound measurement:
Sound Intensity and Sound Pressure Level (SPL).

Sound Intensity (acoustic intensity or energy) drops with the ratio 1/r squared of the distance
and this conforms to the
Inverse Square Law.

Of more interest to us though, is Sound Pressure Level.
Sound Pressure Level decreases with the doubling of distance
by 1/2 of the initial value of the Sound Pressure Level (-6dB).

The sound pressure drops with the ratio 1/r of the
distance and this is known as the
Inverse Distance Law.

Conversely, for us, it means that if you can halve the distance
between the microphone and the sound source,
the sound source SPL will be
2 times greater or double (+6dB).

The Truth about ALDs - Inverse Distance Law

In most listening environments there is some background noise which often shares the same frequencies as the sounds we want to hear. Much of this background noise can be reverberation or just from a general non-specific source.

Imagine a person that you are trying to hear is standing in front of you at about 2 metres away and your microphone is sitting in or on your ear. If you could take the microphone from its present position and place it halfway between the two of you, you would double the SPL of their voice.

Essentially the SPL of the background noise would be the same at your ear and at the halfway point, so this microphone relocation has
positively increased the SNR
(the SPL of the
sound you want to hear relative to the SPL of the background noise).
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Last update 30 June 2022
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