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 ):

Question

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 ):, 6 - 12, 12 - 18, 3 - 6, 18 - 22

MARKS App · Accepted Answer

λ = 320 1280 = 0 . 25 m Using concept of diffraction of wave b sin θ = 1 . 22 λ sin θ = 25 45 × 1 . 22 = 0 . 678 tan θ = 0 . 93 tan θ = y 2 D y ⇒ 2 Dtan θ time to cross this region = 2 D tan θ speed ⇒ 2 × 8 × 0 . 93 1 . 5 ≃ 9 . 9 sec

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