Question

A person standing near a railway line hears two distinct sounds of a train between time interval 2s.how much is the distance of the train?Velocity of steel=16 times velocity of air{340 m/s}

Answer 1

Distance is 725.33 metres.

Answer 2

If the person standing near a railway line hears two distinct sounds of a train, then the sounds are - one travelling through steel and the another travelling through air.

Let the distance of train be d from the person.
speed of sound in air = 340 m/s
speed of sound in steel = 340 × 16 = 5440 m/s

time taken by sound travelling through steel to reach the person = $t_s$
time taken by sound travelling through air to reach the person = $t_a$

$time= \frac{distance}{speed}\\ \\ t_s= \frac{d}{5440} \\ \\t_a= \frac{d}{340}$

given that $t_a - t_s=2$

$\frac{d}{340}-\frac{d}{5440}=2\\ \\d( \frac{1}{340} - \frac{1}{5440} )=2\\ \\d(\frac{16-1}{5440})=2\\ \\d=\frac{2*5440}{15}=725.33\ m$

Distance of train is 725.33 m.