Question

A certain siren radiates sound uniformly in all directions. At a distance of 17 m from the siren, the intensity level is 49 db. How many watts of power does this siren put out? The threshold of human hearing is 1.0 × 10-12 W/m2.

Answer 1

Answer:

The power is  $P = 2.88*10^{-4 } \ W$

Explanation:

From the question we are told that

   The distance from the siren  is  $d = 17 \ m$

  The intensity level is  $\beta = 49\ dB$

   The threshold of hearing is   $I_0 = 1.0 *10^{-12} \ W/m^2$

Generally the intensity level is mathematically represented as

      $\beta = 10dB * log [\frac{I}{I_o} ]$

Where I is the intensity at which the siren radiates the sound

substituting values  

       $49 = 10 * log [\frac{I}{1.0 *10^{-12}} ]$

=>    $I = 7.94*10^{-8} W/m^2$

Now the amount of power the siren put out is mathematically evaluated as

      $P= IA$

Where A is the area  of the siren which is taken as a sphere  and it  is mathematically evaluated as

       $A = 4 \pi d^2$

So  

     $P = I * 4 \pi d^2$

substituting values

    $P = 7.94 *10^{-8} * 4 * 3.142 * (17)^2$

   $P = 2.88*10^{-4 } \ W$