Question

A girl standing infront of a wall at a distance of 90 m produces 2 claps per second she notices that sound of his clapping coincides with the echo. The echo is heard only once when clapping is stopped.
Calculate:—
Speed of sound​

Answer 1

Answer :-

Required speed of sound is 360 m/s .

Explanation :-

We have :-

→ Distance = 90 m

→ Claps produced per second = 2

→ Sound of clapping coincides with the echo.

________________________________

It is given that the girl produces '2 claps in 1 second'. Thus, time taken by each clap is :-

= 1/2

= 0.5 second

________________________________

Now from the formula of echo, we have :-

[Total distance travelled by a wave in time interval 't' is '2d' ].

d = vt/2

Where :-

• d is the distance.

• v is speed of sound.

• t is time taken.

Substituting values, we get :-

⇒ 90 = (v × 0.5)/2

⇒ 90(2) = 0.5v

⇒ 180 = 0.5v

⇒ v = 180/0.5

⇒ v = 360 m/s

Answer 2

Answer:

Given :-

• A girl standing in front of a wall at a distance of 90 m produces 2 claps per second she notices that sound of his clapping coincides with the echo. The echo is heard only once when clapping is stopped.

To Find :-

• What is the speed of sound.

Formula Used :-

$\clubsuit$ Speed of Sound Formula :

$\longmapsto \sf \boxed{\bold{\pink{Speed\: of\: Sound\: =\: \dfrac{Distance\: Travelled}{Total\: time\: taken}}}}$

Solution :-

First, we have to find the distance :

Let,

$\mapsto$ Distance = d m

Hence, the sound has to travel a distance.

So,

$\implies \sf Distance\: travelled =\: 2d$

Given :

• d = 90 m

$\implies \sf Distance\: travelled =\: 2(90)\: m$

$\implies \sf Distance\: Travelled =\: 2 \times 90\: m$

$\implies \sf\bold{\purple{Distance\: Travelled =\: 180\: m}}$

Now, we have to find the time taken :

$\mapsto$ A girl standing in front of a wall at a distance of 90 m produces 2 claps per second.

Since, 2 claps are produced in one second.

Therefore, each claps is produced after 1/2 seconds which is equal to the time taken for the echo to be heard.

So,

$\implies \sf Time\: taken =\: \dfrac{1}{2}\: seconds$

$\implies \sf\bold{\purple{Time\: taken =\: 0.5\: seconds}}$

Hence, the time taken is 0.5 seconds .

Now, we have to find the speed of sound :

Given :

$\bigstar$ Distance travelled= 180 m

$\bigstar$ Total time taken = 0.5 seconds

According to the question by using the formula we get,

$\longrightarrow \sf Speed\: of\: Sound\: =\: \dfrac{180}{0.5}$

$\longrightarrow \sf Speed\: of\: Sound =\: \dfrac{180}{\dfrac{5}{10}}$

$\longrightarrow \sf Speed\: of\: Sound =\: \dfrac{180}{1} \times \dfrac{10}{5}$

$\longrightarrow \sf Speed\: of\: Sound =\: \dfrac{\cancel{1800}}{\cancel{5}}$

$\longrightarrow \sf Speed\: of\: Sound =\: \dfrac{360}{1}$

$\longrightarrow \sf\bold{\red{Speed\: of\: Sound =\: 360\: m/s}}$

$\therefore$ The speed of sound is 360 m/s .