Question

Suppose A and B in the previous problem change their positions in such a way that the line joining them becomes perpendicular to the direction of wind while maintaining the separation x. What will be the time lag B finds between seeing and hearing the drum beating by A ?Concept of Physics - 1 , HC VERMA , Chapter "Rest and Motion : Kinematics

Answer 1

Solution 
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Given, Velocity of sound=v m/s
Velocity of air=u m/s
Velocity of sound be in direction ABC , so that it can reach B with resultant velocity.
Angle between v and u is θ>π/2
Resultant AD= √v²-u²
Here time taken by light to reach B is neglected.
∴Time log between seeing and hearing =time to here the drum sound
t=displacement/velocity =x/√v²-u²
=x/√(v+u)(v-u)
=x/√(x/t1)(x/t2)
[∴speed=v+u=distance/time=x/t1
v-u=x/t2]

t=√t1t2

∴the time lag B finds between seeing and hearing the drum beating by A is√t1t2