Question

A band is playing at the Falls Festival. The stage is 1.5m off the ground and there is a flat wall behind them. The sound radiates out from the band, acting like a spherical sound source, and the audience does not reflect any of the sound. If the sound pressure levels 45m from the band are measured at 120dBA, how far from the band do you need to be standing to have the sound loudness double? *Please note: The Directivity Index for a flat wall at the center of a surface can be approximated as 3

Answer 1

Sound level or noise level is a physical quantity measured with measuring instruments.
Loudness is a psycho-physical sensation perceived by the human auditory perception or the human ear/brain mechanism. That is not the same.
We are told by psycho-acousticians that a level 10 dB greater usually means "double the loudness" or "twice as loud".

dBA levels are "A" weighted according to the weighting curves to approximate the way the human ear hears.

The directivity index (Di) is an expression in decibels of the directionality of a sound source. Narrow coverage systems have a high directivity index, whereas wide coverage systems have a low one. Di is the decibel form of directivity Q factor, so both are related as Di = 10*log(Q).

the sound pressure p doesn't decrease with the square of the distance
from the sound source (1/r²).