Question

single goose sounds a loud warning when an intruder enters the farmyard. Some distance from the goose, you measure the sound level of the warning to be 81.0 dB. 1) If a gaggle of 26 identical geese is present, and they are all approximately the same distance from you, what will the collective sound level be if they all sound off simultaneously

Answer 1

Answer:

The sound level of the 26 geese is  $Z_{26}= 96.15 dB$

Explanation:

From the question we are told that

    The  sound level is $Z_1 = 81.0 \ dB$

     The number of geese is $N = 26$

Generally the intensity level of sound is mathematically represented as

        The intensity of sound level in dB  for one  goose is mathematically represented as

                       $Z_1 = 10 log [\frac{I}{I_O} ]$

Where I_o is the  threshold level of intensity with value  $I_o = 1*10^{-12} \ W/m^2$

            $I$ is the intensity for one goose in $W/m^2$

For 26 geese the intensity would be  

          $I_{26} = 26 * I$

   Then  the intensity of 26 geese in dB is  

              $Z_{26} = 10 log[\frac{26 I }{I_o} ]$

               $Z_{26} = 10 log (\ \ 26 * [\frac{ I }{I_o} ]\ \ )$

               $Z_{26} = 10 log (\ \ 26 \ \ ) * (\ \ 10 log [\frac{ I }{I_o} ]\ \ )$

 From the law of logarithm we have that

              $Z_{26} = 10 log 26 + 10 log [\frac{I}{I_0} ]$

                    $= 14.15 + 82$

                    $Z_{26}= 96.15 dB$