How long will sound take to travel in (a) an iron rail and (b) air, both 3.3 km in length? Take speed of sound in air to be 330 m s^-1 and in iron to be 5280 m s^-1 .

(a) Given,

Length of the iron rail = 3.3 km

Converting km to m, we get,

1 km = 1000 m

Therefore, 3.3 km = 1000 x 3.3 = 3300 m

Speed of the sound in iron (V) = 5280 m s^-1

t = ?

V = $\dfrac{\text{Distance (d)}}{\text {Time (t)}}$

Substituting the values, we get,

$5280 = \dfrac{3300}{t} \\[0.5em] \Rightarrow t = \dfrac{3300}{5280} \\[0.5em] \Rightarrow t = 0.625 \text { s} \\[0.5em]$

Therefore, the time taken by sound to travel in iron rail = 0.625 s

(b) Speed of sound in air = 330 m s^-1

Substituting the values in the above formula, we get,

$330 = \dfrac{3300}{t} \\[0.5em] \Rightarrow t = \dfrac{3300}{330} \\[0.5em] \Rightarrow t = 10 \text { s} \\[0.5em]$

Therefore, the time taken by sound to travel in air = 10 s