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A Weather Emergency Siren Is Mounted on a tTower

A weather emergency siren is mounted on a tower, 177 meters above the ground. On one hand, it would be a good idea to make the siren very loud so that it will warn as many people as possible. On the other hand, safety regulations prohibit the siren from exceeding an intensity level of 101 dB for workers standing on the ground directly below the siren.

  1. Assuming that the sound is uniformly emitted, what is the maximum power P that the siren can emit?
  2. How far from the base of the tower can a person be and still be able to hear the siren?

Note: Neglect any absorption of sound energy by the air. In reality, such absorption would be significant at long distances.

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1 Answer

    • The maximum power P that the siren can emit is approximately 1577.55 W.
    • The distance ddd from the base of the tower that a person can be and still hear the siren is approximately 1.12 \times 10^7 meters (which is about 11,200 kilometers, a theoretical value since in reality, sound absorption and other factors would significantly reduce this distance).