Sunil is standing between two walls. The wall closest to him is at a distance of 360 m. If he shouts, he hears the first echo after 4 s and another after another 2 seconds. (Ans: 330 m/s; 1650 m). Solve the example.
1. What is the velocity of sound in air?
2. What is the distance between the two walls?
Answers
1. Distance between the closest wall and Sunil = 360 m.
Time taken by the Sunil to heard the Echo = 2 s.
[∵ Echo will be heard in less time when the wall is close.]
∵ v = 2d/t
⇒ v = 2 × 360/2
∴ v = 360 m/s.
2. Let the total distance between the two walls be 'd' m.
∴ Distance between the Sunil and Distant wall = (d - 360) m
Time taken for the Echo to heard = 4 s.
Speed of the sound in air = 360 m/s.
∴ 360 = 2 × (d - 360)/4
⇒ d - 360 = 360 × 2
∴ d = 720 + 360
⇒ d = 1020 m.
Hence, the distance between the two walls is 1020 m.
Hope it helps.
Correct question:
- Sunil is standing between two walls the wall closest to him is at a distance of 660m if he shouts he hears the first echo after 4s and another after another 2 seconds.
Find
i) Velocity of sound in Air ?
ii) Distance between two walls
(As this question is from State board; And, It by printing mistake in some books, The distance is given as 360 meters; And answer is also given there as 330 and 1650 respectively; So, if we solve this problem by considering distance 360 meters, then answer will get wrong).
Answer:
Velocity = 330m/s
Distance between two walls = 1650 meters
Given information:
Suppose sunil is standing is a room between 2 walls.
Wall closest to sunil is at distance of 660 meters.
And, If he shouts, then he heard the Echo from his nearest wall in 4 seconds.
And, Another wall echo is heard in next 2 seconds.
To find: i) Velocity of sound in Air ?
ii) Distance between two walls
Explanation:
Method I :
i) Velocity of sound in Air:
Velocity = Distance / Time/2 (Because we heard sound after getting reflected back)
Velocity = 660 / 2
Velocity = 330 m/s
Therefore, Velocity of sound in Air is 330 m/s.
ii) What is the distance between two walls ?
For first wall,
Distance = ?
Velocity = 330 m/s
Time = 4 seconds
Distance = Velocity * time
Distance = 330 * 4
Distance = 1320 meters -------- (i)
For second wall,
Distance = ?
Time = 2 seconds
Velocity = 330 m/s
Distance = Velocity * 2/ time
Distance = 330 * 1
Distance = 330 meters ------- (ii)
Adding equation (i) and (ii),
Distance between 1st wall + Distance between 2nd wall = Distance between two walls
Distance between two walls = 1320 + 330
Distance between two walls = 1650 meters
Therefore, Distance between 2 walls is 1650 meters.
Method II :
i) Velocity of sound:
Velocity of sound = Distance/time
Velocity of sound = 660/2
Velocity of sound = 330 m/s
ii) Distance between two walls:
Distance = Velocity * total time
Distance = 330 * 6
Distance = 1650 meters