Question

A man fires a gun while standing between two parallel hills. If he hears the first echo after 2 s and the second echo 3 s after the first echo, then calculate the distance between the hills the velocity of sound is 330 m/s.

Answer 1

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Let d be the distance of first hill , which gives an echo after 3/2s and d

′

be the distance of another hill which gives echo after 5/2s , from the person .

given , speed of sound =332m/s

now for echo from first hill ,

total distance travelled by sound =2d , (distance is doubled as the sound comes back to person after reflection)

total time taken by sound =3/2s , to travel a distance of 2d,

hence , distance=speed×time ,

2d=332×(3/2) ,

or d=249m ,

for echo from another hill ,

total distance travelled by sound =2d

′

, (distance is doubled as the sound comes back to person after reflection)

total time taken by sound =5/2s , to travel a distance of 2d

′

,

hence , distance=speed×time ,

2d

′

=332×(5/2) ,

or d

′

=415m ,

therefore total distance between hills =249+415=664m .

Third echo will be heard when sound coming to person after reflection from first hill (first echo) goes toward another hill and reflects back to person again ,

time taken by sound to reflect back to person from first hill (first echo) =3/2s ,

time taken by sound to reflect back to person from another hill =5/2s ,

therefore , total time (for third echo) =(3/2)+(5/2)=4s .

Answer 2

Explanation:

1st case

first echo is heard in 2 sec.

so time period is 2 s

speed =330 m/s

distance=speed×time=660m

2nd case

2nd echo takes 3 sec.

speed same

distance=330×3=990

total distance=990+660=1650 m