Question

A train approaching a railway crossing at a speed of $180km{h}^{-1}$ sounds a short whistle at a frequency $600Hz$, when it is $400m$ away from the crossing. The speed of sound in air is $340{ms}^{-1}$. The frequency of the sound heard by a person standing on a road perpendicular to the track at a distance of $300m$ from the crossing is:

• A. $680Hz$
• B. $480Hz$
• C. $40Hz$
• D. $50Hz$

Answer 1

The correct option is A $680Hz$

When a source is moving in a direction making an angle w.r.t. a stationary observer , then apparent frequency heard by observer is given by ,

$n^{\prime }=n\left(\frac{v}{v-v_s\cos \theta }\right)$

Here , $v_s=180km/h=180\times 5/18=50m/s$

$n=600Hz$

$v=340m/s$

From figure , we get

$\cos \theta =4/5$

Therefore ,

$n^{\prime }=600\left(\frac{340}{340-50\times \left(4/5\right)}\right)$

or $n^{\prime }=680Hz$