Question

A person standing between two parallel hills fires a gun. He hears the first echo after (3) /(2) s, and a second echo after (5) /(5) s. If speed of sound is 332 m//s , Calculate the distance between the hills. When will he hear the third echo?

Answer 1

The distance between the hills = 664 meter.

Total time (for third echo) = 4 sec.

Given:

• A person standing between two parallel hills fires a gun.
• He hears the first echo after $\frac{3}{2}$ s.
• A second echo after $\frac{5}{2}$  s.
• Speed of sound is 332 m/s

To find:

• The distance between the hills.
• When will he hear the third echo.

Explanation:

• Let "d" is the distance of first hill.
• "D" is the distance of second hill.
• He hears the first echo after $\frac{3}{2}$ seconds at first hill.
• He hears the second echo after $\frac{5}{2}$ seconds at second hill.

From the given data,

Sound travelling speed = 32 m/s

He hears the first echo after $\frac{3}{2}$ seconds at first hill :

Distance traveled by sound = d.

Note : Distance will be doubled, when sound return back to the person after reflection.

Total distance traveled by sound = 2d.    

Total time taken by sound = $\frac{3}{2}$ seconds.

Formula used :

Distance = Speed × Time.

2d = 332 × $\frac{3}{2}$

d = 249 m.

He hears the second echo after $\frac{5}{2}$ seconds at second hill :

Distance traveled by sound = D.

Total distance traveled by sound = 2D.    

Total time taken by sound = $\frac{5}{2}$  seconds.        

Formula used :

Distance = Speed × Time

2D = 332 $\times \frac{5}{2}$

D = 415 m.

The distance between two hills :

Total distance covered between two hills = d + D

                                                                     = 249 + 415

Distance between two hills = 664 m.

Third echo can be heard by the person when the sound reflects back from the first hill. This is the same process for second hill, which return back to the person again.

Sound reflect back to the person from first hill :

Time taken = $\frac{3}{2}$ seconds

Sound reflect back to the person from second hill :

Time taken = $\frac{5}{2}$ seconds.

Total time taken for third echo :

Time taken = $\frac{3}{2}$ + $\frac{5}{2}$

                   = $\frac{8}{2}$

Time taken = 4 seconds.

Therefore, the person will hear the third echo in 4 seconds.

To learn more...

1) A sound wave travels 2000m in 8second. What is the velocity of the sound.

brainly.in/question/14493071

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