Question

A train is traveling at 30.0 m/sm/s relative to the ground in still air. The frequency of the note emitted by the train whistle is 262 HzHz. The speed of sound in air should be taken as 344 m/sm/s.A. What frequency fapproach is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and approaching it?B. What frequency frecede is heard by a passenger on a train moving at a speed of 18.0 m/s relative to the ground in a direction opposite to the first train and receding from it?

Answer 1

Answer

given,

speed of sound = 344 m/s

speed of train = 30 m/s

frequency emitted by the train = 262 Hz

   Doppler's effect

    $f_L = \dfrac{v + v_L}{v + v_s}\ f_S$

f_L is the frequency of listener

f_S is the frequency of the source of the sound

v is the speed of the sound

v_L is the speed of listener.

v_S is the speed of the source

a) Speed of the passenger in another train , v = 18 m/s

   another train is moving in opposite direction and approaching

   v_L is positive as the listener is moving forward.

    v_S is negative at the source is moving toward the listener.

      $f_L = \dfrac{344 + 18}{344 - 30}\times 262$

     $f_L = 302\ Hz$

b) Speed of the passenger in another train , v = 18 m/s

   another train is moving in opposite direction and receding

    v_L is negative as the listener is moving away from source.

    v_S is positive at the source is moving away the listener.

      $f_L = \dfrac{344 - 18}{344 + 30}\times 262$

     $f_L = 228.37\ Hz$