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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?

Solution
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Listener will not perceive twice loudness.
Loudness formula is given by L=10logI/I0,
Let initial loudness be L and initial intensity be I, since now intensity is doubled new loudness will be given by
L=10log2I/I0
L=10×log2+logI/I0
Clearly it is not that twice of initial value.

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