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30 June, 01:33

An aircraft maintenance technician walks past a tall hangar door that acts like a single slit for sound entering the hangar. Outside the door, on a line perpendicular to the opening in the door, a jet engine makes a 610 Hz sound. At what angle with the door will the technician observe the first minimum in sound intensity if the vertical opening is 0.840 m wide and the speed of sound is 340 m/s

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  1. 30 June, 02:46
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    The first minimum would be observed at 41.57°

    Explanation:

    v = 340m/s = speed of sound

    f = 610Hz

    d = 0.840m

    λ = ?

    Mλ = wsinθ

    m = mth order minima

    λ = wavelength incident on the single slit

    θ = angular position of the mth minima

    But, λ = v / f

    λ = 340 / 610 = 0.557m

    θ = sin⁻ (mλ/d)

    θ = sin⁻ [ (1 * 0.557) / 0.840]

    θ = sin⁻ 0.6635

    θ = 41.57°

    The first minimum would be observed at 41.57°
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