Concepts Of Physics MCQ Edition [Volume 1]PhysicsRest and Motion Kinematics
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 seeing the event. A and B swap their positions and the experiment is repeated. This time, B hears the drum t₂ time after seeing the event. Determine the velocity of sound in still air v and the velocity of wind u . Neglect the time light takes to travel between the
Options
- Av = 2x t₁ + t₂ , u = 2x t₁ - t₂
- Bv = x 2 ( 1 t₁ + 1 t₂ ) , u = x 2 ( 1 t₁ - 1 t₂ )
- Cv = x 2 ( 1 t₁ - 1 t₂ ) , u = x 2 ( 1 t₁ + 1 t₂ )
- Dv = x ( 1 t₁ + 1 t₂ ) , u = x ( 1 t₁ - 1 t₂ )
Correct answer
B. v = x 2 ( 1 t₁ + 1 t₂ ) , u = x 2 ( 1 t₁ - 1 t₂ )
Step-by-step solution
Let v be the velocity of sound in still air and u be the velocity of wind. In the first case, the wind blows from A to B . The velocity of sound relative to the ground is v + u . The time taken for sound to travel distance x is t₁ = x v + u . v + u = x t₁ In the second case, A and B swap positions. The sound now travels from the new position of A to the new position of B , which is opposite to the direction of the wind. The velocity of sound relative to the ground is v - u . The time taken for sound to travel dista