Question

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.
What is the velocity of sound in
air?
What is the distance between the
two walls?
(Ans: 330 m/s; 1650 m)​

Answer 1

Answer:

Given:

Distance of nearest wall from the man (d) = 360m

Time after which the man hears the first echo (t1) = 4s

Time after which the man hears the second echo (t2) = 4s+2s = 6s

1.Distance travelled by sound when man hears the first echo = 2d1 = 720m

Velocity of sound = Distance travelled by sound/Time taken

= 720/4

= 180 m/s

2. Let distance between two walls = x m

Distance between second wall and the man(d2) = (x-360)m

Time taken for the second echo to reach the man (t2) = 6s

Distance travelled by the sound = 2d2

Velocity of sound = Distance travelled by sound/Time taken

180 = (2(x-360))/6

x = 900 m

Therefore, distance between the two walls (x) = 900m

Answer 2

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 .

(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