How Distance Affects Sound Level

How sound intensity varies with distance is simple in principle if you are talking about a symmetrical sound source with no surfaces for sound to reflect off. The intensity of the sound decreases as the inverse square of the distance, as its power is spread over the surface of an ever-increasingly large sphere. In reality, things are more complex, with directional loudspeakers defining a prefered axis, and surfaces for sound to reflect off creating echoes. In this case, the rule is approximate, if still useful. This rule also means that as you get very close to a loudspeaker the sound intensity rises dramatically. This is why loudspeakers should ideally be situated at some distance from the audience so that the sound level varies less dramatically across the intended listening area.

What Do We Hear?

But sound intensity isn't the end of the story because we are talking about sounds as perceived by our ears. Our ears and sense of hearing are capable of withstanding very intense (loud) sounds, and also extremely quiet sounds in the absence of any other. Consider the fact that you can appreciate both loud rock music at a concert and the rustling of a leaf on a cold quiet day. This is why sound levels as heard by humans are represented by a logarithmic scale – the decibel scale. Using the simple rule a doubling of the distance will approximately reduce sound intensity by a factor of 4, which translates to a drop by 6db. But a drop of 10db is required for a sound to be perceived by us as being half as loud. So the answer is that it changes less than you might expect, because of how we process sound.