Question

a student stands several meters in front of a smooth reflecting wall, holding a board on which a wire is fixed at each end. the wire, vibrating in its third harmonic, is 75.0cm long, has a mass of 2.25g, and is under a tension of 400 N. a second student, moving towards the wall, hears 8.30 beats per second. what is the speed of the student approaching the wall? (solve without calculus)

Answer 1

Answer:

Explanation:

From the question we are told that

      The length of the wire is  $L = 75.0cm = \frac{75}{100} = 0.75 \ m$

      The mass of the wire is  $m = 2.25 \ g = \frac{2.25}{1000} = 0.00225 \ kg$

      The tension is  $T = 400 \ N$        

       The frequency of the beat heard by the second student is

  $f_b = 8.30\ beat/second$

The speed of the wave generated by the vibration of the wire is mathematically represented as

           $v = \sqrt{\frac{TL}{m}}$

substituting values

           $v = \sqrt{\frac{400 *0.75}{0.00225}}$

          $v = 365.15 m/s$

         The wire is vibrating in its third harmonics so the wavelength is  

                        $\lambda = \frac{2L}{3}$

substituting values

                        $\lambda = \frac{2*0.75}{3}$

                        $\lambda = 0.5 \ m$

The frequency of this vibration is mathematically represented as  

              $f = \frac{v}{\lambda }$

substituting values  

           $f = \frac{365.15}{0.5 }$

          $f = 730.3 Hz$

The speed of the second student (Observer) is mathematically represented as

           $v_o = [\frac{f_b}{2f} ] * v$

substituting values    

         $v_o = [\frac{8.30}{2* 730.3} ] * 365.15$

        $v_o = 2.08 \ m/s$