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Most Important Selected Qs for JEE AdvancedPhysicsWaves and Sound

Paragraph: At a time t=0 a pulse moving in the +v e x -direction with velocity v in the shape given by the function between with y= array ll x 4 +1 & -4 x 0 -x+1 & 0 x 1 0 & otherwise array . , where x and y are in cm . Question: Velocity of a point at x=20 ~m as a function of time is given as

Options

  1. Av= cases 1 4 ~m / s & 1.999 t 2 ~s -1 ~m / s & 2 t 2.004 ~s 0 & otherwise cases
  2. Bv= cases 1 ~m / s & 1.999 t 2 ~s - 1 4 ~m / s & 2 t 2.004 ~s 0 & otherwise cases
  3. Cv= cases 10 ~m / s & 1.999 t 2 ~s - 5 2 ~m / s & 2 t 2.004 ~s 0 & otherwise cases
  4. Dv= cases 5 2 ~m / s & 1.999 t 2 ~s -10 ~m / s & 2 t 2.004 ~s 0 & otherwise cases

Correct answer

C. v= cases 10 ~m / s & 1.999 t 2 ~s - 5 2 ~m / s & 2 t 2.004 ~s 0 & otherwise cases

Step-by-step solution

At t =0 velocity of wave =10 ~m / s . Thus pulse get shifted by (10 10⁻³ ) m Wave equation; obtained by replacing x by ( x-v t ) Pulse reaches x =20 ~m at t =2 sec First half of the wave reaches at t =1.999 sec ; V = particle = d x d t =v_ wave =10 ~m / s Second half of the wave reaches at t =2 & leaves at t =2.004 sec ; V = 1 4 d x d t =- 5 2

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