Question

If a 15 - person musical group has 15 new members, so that its size doubles, will a listner perceive the music created by the group to be twice as loud? Why or why not?

Answer 1

Listener will not perceive twice loudness.
Loudness formula is given by $L=10logI/I_0$,
Let initial loudness be $L$ and initial intensity be $I$, since now intensity is doubled new loudness will be given by
$L^{{}^{\prime }}=10log2I/I_0$
$L^{{}^{\prime }}=10\times log2+logI/I_0$
Clearly it is not that twice of initial value.