Question

A train approaching a railway crossing at a speed of $ 120 \,km/h $ sounds a whistle at frequency $ 640 \,Hz $ when it is $ 300\, m $ away from the crossing. The speed of sound in air is $ 340 \,m/s $ . What will be the frequency heard by a person standing on a road perpendicular to the track through the crossing at a distance of $ 400\, m $ from the crossing?

• A. 680 Hz
• B. 640 Hz
• C. 720 Hz
• D. 358 Hz

Answer 1

Answer: (A)

$v_s = 120\,km/h = \frac{100}{3} m/s$

$ n = 640 \,Hz$ and $ v= 340\,m/s$
$n'= n \left(\frac{v}{v-v_{s} \,cos\,\theta}\right) $
$ = 640 \left(\frac{340}{340 - \frac{100}{3}\times \frac{300}{500}}\right) $
$ n' = 680 \,Hz$