A person standing between two hills fired a gun and heard the first echo after 0.5 seconds and the second echo after 0.9 seconds. Find the distance between the two hills
Answers
Answer:
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: