How many times closer does a listener need to be to receive a 12 dB gain according to the Inverse Square Law?

To achieve a 12 dB gain in sound intensity, the listener needs to be 4 times closer to the sound source. The Inverse Square Law states that sound intensity decreases with the square of the distance from the source. Specifically, a change of 6 dB corresponds to a doubling of distance. Therefore, a 12 dB increase indicates that the intensity is four times greater than it would be at a certain reference distance. This is because:

1. A 6 dB increase means that the distance has been halved, hence the listener is at half the distance to sound source.

2. A second 6 dB increase (for a total of 12 dB) means halving the distance again.

By halving the distance twice, we find that the listener is now 4 times closer to the sound source than at the original distance to achieve that 12 dB gain. This understanding aligns with the principles of sound propagation and the effects of distance on sound intensity.