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)

$680 \,Hz$

Answer 2

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

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