Q89 / 91 · KVPY 2020 (SB/SX) · Physics

A student is jogging on a straight path with the speed 5.4 km per hour. Perpendicular to the path is kept a pipe with its opening 8 m from the road (see figure). Diameter of the pipe is 0.45 m At the other end of the pipe is a speaker emitting sound of 1280 Hz towards the opening of the pipes. As the student passes in front of the pipe, she hears the speaker sound for T seconds. T is in the range (take speed of sound, 320 ms-1):

Figure

  • Correct answer
    A
    6-12
  • B
    12-18
  • C
    3-6
  • D
    18-22

Solution

Figure

λ=3201280=0.25 m

Using concept of diffraction of wave

bsinθ=1.22λ

sinθ=2545×1.22=0.678

tanθ=0.93

tanθ=y2D

y⇒2Dtanθ

time to cross this region =2Dtanθ speed 

⇒2×8×0.931.5≃9.9sec

Hence, the correct answer is option: 'A'.

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