The distance to a point source is decreased by a factor of three. by what multiplicative factor does the intensity increase? By what additive amount does the intensity level increase?
As the sound energy is spread over the AREA of the surface, 1/3 distance gives 1/9 area
and 9 times the intensity.
You don't want to know the additive amount.
It isn't possible for the information given here.
You actually want to know the dB change.
by definition the decibel is 10 log ( change) ( using log to the base 10 hard to write here)
Which for a change of 9 becomes 10* log (9) = 9.54 dB
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As the sound energy is spread over the AREA of the surface, 1/3 distance gives 1/9 area
and 9 times the intensity.
You don't want to know the additive amount.
It isn't possible for the information given here.
You actually want to know the dB change.
by definition the decibel is 10 log ( change) ( using log to the base 10 hard to write here)
Which for a change of 9 becomes 10* log (9) = 9.54 dB