On a whale-watching expedition, your underwater sound detector picks up a whale

Question

On   a   whale-watching   expedition,   your   underwater   sound   detector   picks   up   a   whale   sound  
that   has   an   intensity   of   9.0   ?W/m2

(a)   What   is   the   intensity   level   ?   of   this   sound?      

(b)   If   your   detector   tells  
you   that   you   are   2.3   km   from   the   whale,   what   is   the   power   of   the   emitted   signal?       (c)   How   many   whales,  
emitting   sound   at   the   same   intensity   I   =   9.0   ?W/m2,   are   needed   to   produce   an   intensity   level   of   100dB   at   your   location?  

Explanation / Answer

apply Intensity I = power/area

and Intensioty level = B = 10 dB log ( I./Io)

where Io = 10^-12 W/m^2   constant

so

a. Inentsity Level = 10 dB * log ( 9/10^-12)

= 129.54 decibels

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b., apply I    = P/A

so   Power P = IA    = 9 * 4pi * 2300*2300

P = 5.97 *10^8 Watts

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c.   N = 129.54/100 = 1.3 whales

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