Question

A train standing at the outer signal of a railway station blows a whistle of frequency $400 \,Hz$ in still air. The train begins to move with a speed of $30\, m\, s^{-1}$ towards the platform. The frequency of the sound heard by an observer standing on the platform is (Speed of sound in air = $330\,m \, s^{-1})$

• A. $420\, Hz$
• B. $430\, Hz$
• C. $440 \, Hz$
• D. $450 \, Hz$

Answer 1

Answer: (C)

$440 \, Hz$

Answer 2

Here, Frequency of source, $\upsilon=400\, Hz$ Speed of sound, $v = 330 \, m \, s^{-1}$ Speed of source (i.e. train), $\upsilon_{s}=30\, m\,s^{-1}$ As the source is moving towards stationary observer $\therefore \upsilon' =\frac{\upsilon v}{v-v_{s}}=\frac{\left(400\,Hz\right)\times\left(330\,m\,s^{-1}\right)}{330\,m\,s^{-1}-30\,m\,s^{-1}}$ $=440\,Hz$