Question

Sonar is used to determine the speed of an object. A 38.0-kHz signal is sent out, and a 40.0-kHz signal is returned. If the speed of sound is 341 m/s, how fast is the object moving?

Answer 1

Answer:

The velocity is  $v = 8.743 \ m/s$

Explanation:

From the question we are told that

    The frequency of the signal sent out  is  $f_s = 38.0 \ kHz = 38.0 *10^{3} \ Hz$

    The frequency of the signal received is  $f_r = 40.0 \ kHz = 40.0 *10^{3} \ Hz$

     The  speed of sound is  $v_s = 341 \ m/s$

Generally the frequency of the sound received is  mathematically represented as

         $f_r = f_s [\frac{v_s + v}{v_s - v} ]$

where v is the velocity of the object

       =>      $40 *10^{3} = 38 *10^{3} * [\frac{341 + v}{341 - v} ]$

       =>      $1.05263 = \frac{341+v }{341-v}$

       =>   $358.94 - 1.05263v = 341 + v$

      =>    $17.947 = 2.05263 v$

      =>    $v = 8.743 \ m/s$