Question

Residents of Hawaii are warned of the approach of a tsunami by sirens mounted on the tops of towers. Suppose a siren produces a sound that has an intensity level of 120 dB at a distance of 2.0 m.

Part A: Treating the siren as a point source of sound, and ignoring reflections and absorption, find the intensity level heard by an observer at a distance of 12 m from the siren.

Part B: Treating the siren as a point source of sound, and ignoring reflections and absorption, find the intensity level heard by an observer at a distance of 21 m from the siren.

Part C: How far away can the siren be heard?

Answer 1

The definition of the intensity level is
  
where, is the intensity of the reference level.
This implies
  
The intensity level at a distance r_1 = 2.0 m is . And so, the sound intensity at this level is
   
And as intensity at a distance r follows the inverse square law of distance, i.e.,
   
  
  
Part - A :

  Given , we have
  
  
And so, for the distance , we have the sound intensity at this distance 12 m,
  
And the intensity level for this is given by
   
  

Part - B :
  For the distance , we have the sound intensity at this distance 21 m,
  
And the intensity level for this is given by
   
  

Part - C :
   The Siren can be heard let say upto a distance where, the intensity level is zero. Which implies
  
  
  
  
And so, from the result
   , we have