Discussion Forum

A train moving on a straight track with speed 20 ms^-1. It is blowing its whistle at the frequency of 1000Hz. The percentage change in the frequency heard by a person standing near the track as the train passes him is  close to (speed of sound =320 ms^-1  )

Answer:

Explanation:

 Apparent frequency heard by the person before crossing the train.

    $f_{1}=\left(\frac{c}{c-v_{s}}\right)f_{0}=\left(\frac{20}{320-20}\right)1000$

  Similarily, apparent frequency heard , after crossing the trains

  $f_{2}=\left(\frac{c}{c+v_{s}}\right)f_{0}=\left(\frac{20}{320+20}\right)1000$

                                                     [c=speed of sound]

    $\triangle f= f_{1}-f_{2}=\left(\frac{2cv_{s}}{c^{2}-v_{s}^{2}}\right)f_{0}$

        or      $\frac{\triangle f}{f_{0}}\times100=\left(\frac{2cv_{s}}{c^{2}-v_{s}^{2}}\right)\times 100$

               $=\frac{2\times320\times20}{300\times340}\times100$

                         $=\frac{2\times32\times20}{3\times34}=$   12.54%=12%