Question

How long will sound take to travel in (a) an iron rail and (b) air, both 3.3km in length respectively? Take speed of sound in air to be 330m/s in an iron to be 5280m/s.
A. (a) 0.625s, (b) 10s
B. (a) 10s, (b) 0.625s
C. (a) 0.625s, 9b) 0.625s
D. None of the above

Answer 1

Hint: Speed is defined as the distance covered per unit time. It is directly proportional to the distance travelled and inversely to the time taken. i.e. speed = distance/time; Time = distance/speed; Distance $ \times $time. In order to solve the question, write down all the given physical quantities and apply the formula of speed we can find the required solution.
Formula Used: Time taken = $\dfrac{{{\text{Distance}}}}{{{\text{speed}}}}$

Complete answer:
(a) In iron rail:
We know that time is calculated by, Time taken = $\dfrac{{{\text{Distance}}}}{{{\text{speed}}}}$
Now, here it is given that the speed of sound in an iron to be 5280m/s, distance to cover is 3.3km in length.
Converting the distance in km to metre we will get a distance of 3300m.
So, Time taken to complete the distance in an iron rail = $\dfrac{{3300}}{{5280}} = 0.625s$
(b) In air:
Similarly, in the air also time taken to complete the given distance is given by,
Time taken = $\dfrac{{{\text{Distance}}}}{{{\text{speed}}}}$
Now, here it is given that the speed of sound in the air to be 330m/s, distance to cover is 3.3km in length.
Converting the distance in km to metre we will get a distance of 3300m.
So, Time taken to complete the distance in the air = $\dfrac{{3300}}{{330}} = 10s$
Thus, it will take sound (a) 0.625s in a rail to travel a distance of 3.3km. Similarly, it will take sound (b) 10s in the air to travel a distance of 3.3km.

Hence, option (A) is the correct answer.

Note:
The speed of sound varies greatly depending upon the medium it is travelling through. The more rigid is the medium, faster the speed of the sound would be. Sound is a mechanical wave i.e. it needs a medium to travel.