KVPY 2020-21 SB SX Exam Previous Papers

Question : 98 of 120

Marks: +1, -0

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 m/s) :

6-12
12-18
3-6
18-22

Validate

Solution:

\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 {D} \tan \θ

time to cross this region

={2 {D} \tan \θ}/{\text " speed "}

\⇒{2 \×8 \×0.93}/{1.5} \≃9.9 {\sec}

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