Sound with frequency 1200 HzHz leaves a room through a doorway with a width of 1.03 mm . At what minimum angle relative to the centerline perpendicular to the doorway will someone outside the room hear no sound

Explanation:

The problem is based on diffraction of sound . In this phenomenon sound does not travel in straight line . It turns around the pointed corner . Due to it,  sound intensity forms fringes ie intensity are not uniformly scattered on all around.

wave length λ = velocity / frequency

= 340 / 1200

λ  = 0.2833 m .

slit width  a = 1.03 x 10⁻³

angular width of central fringe = 2 λ / a

= 2 x .2833 / 1.03 x 10⁻³

= .5666 x 10³ radian .

566.6 radian .

Within this angle intensity of sound is maximum.

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