Question

Two friends A and B are standing a distance x apart in an open field and wind is blowing from A to B. A beats a drum and B hears the sound t1 time after he sees the event. A and B interchange their position and the experiment is repeated. This time B hears the drum t2 time after he sees the event. Calculate the velocity of sound in still air v and the velocity of wind u. Neglect the time light takes in travelling between the friends..Concept of Physics - 1 , HC VERMA , Chapter "Rest and Motion : Kinematics

Answer 1

Solution :
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Let the velocity of sound=v m/s
Let velocity of air=u m/s
Distance between A and B = xm
In first case :
Resultant velocity of sound= u+v

Speed= Distance/ time
(v+u)=x/t1 ---------------(1)

In second case :
Resultant velocity= v-u
Speed = Distance/time
v-u=x/t2---------------(2)
Solving equation 1 and 2 we get :
2v=(x/t1+x/t2)
v=x/2[1/t1+1/t2]
From equation 1 and 2 we get :
u=x/t1 - v
=x/t1-x/2t1-x/2t2
=x/2t1-x/2t2
=x/2[ 1/t1-1/t2]
Velocity of sound in  air v = x/2 [1/t1+1/t2] and
velocity of wind/air =u=x/2[1/t1-1/t2]

Answer 2

x/(v+u) =t1=> v+u=x/t1.......eqn(i.)
& x/(v-u)=t2=> v-u=x/t2...... eqn(ii.)
adding (i) & (ii),
2v=x/t1+x/t2
v=½x[(1/t1)+(1/t2)]
subtracting (ii.) from (i),
2u=(x/t1)-(x/t2)
u= ½x[(1/t1)-(1/t2)]