Question

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear

Answer 1

Answer:

The  values is  $f_b =14.9 \ beats/s$

Explanation:

From the question we are told that

   The  speed of the fire engine is  $v = 5\ m/s$

    The frequency of the tone is  $f = 500 \ Hz$

    The speed of sound in air is $v_s = 340 \ m/s$

The  beat frequency is mathematically represented as

     $f_b = f_a - f$

Where  $f_a$ is the frequency of sound heard by the people in the fire engine and is is mathematically evaluated as

   $f_a = [\frac{v_s + v }{v_s -v} ]* f$

substituting values

  $f_a = [\frac{340 + 5 }{340 -5} ]* 500$

  $f_a = 514.9 \ Hz$

Thus  

      $f_b =514.9 - 500$

      $f_b =14.9 \ beats/s$