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 8m 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 Hx to wards the opening of the pipes. As the student passes in front of the pipe, she hears the speaker for T seconds. T is in the range (Take speed of sound, 320 m/s)

Options

A. `6-12`
B. `12-18`
C. `3-6`
D. `18-22`

Answer

A

Explanation

` lamda = ( 320 )/(1280 ) = 0.25 m`
using concept of diffraction of wave
` b sin theta = 1.22 lamda`
` sin theta = ( 25 )/(45 ) xx 1.22 = 0.678 `
` tan theta = 0.93`
` tan theta = ( y)/( 2D ) `
` Y implies 2D tan theta `
Time to cross this region `= ( 2D tan theta)/("speed")`
`implies ( 2 xx 8 xx 0.93 )/(1.5 ) = 9.9 sec `