Applying the Inverse Square Law, how many times closer must a listener move to hear a presentation with a 12 dB gain?

To determine how many times closer a listener must be to experience a 12 dB increase in sound level, it's essential to understand the principle of the Inverse Square Law. This law states that as you move closer to a sound source, the intensity of the sound increases proportionately to the square of the distance from the source.

A change of 10 dB corresponds to a tenfold increase in intensity. Therefore, an increase of 12 dB indicates that the intensity must exceed the original level significantly more than just a 10 dB increase. In the context of intensity, each doubling of distance results in a reduction of sound intensity by 6 dB.

To achieve a 12 dB increase, we can break it down as follows:

1. From the reference level, increasing by 10 dB, which requires moving four times closer (2^2 = 4, since a doubling happens twice).

2. The additional 2 dB requires moving even closer, which translates to halving the distance again, resulting in a total movement closer by a factor of 8 (2^3 = 8).

Thus, to achieve a 12 dB gain in overall sound level, the listener must move 8 times closer