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15 September, 22:41

A speaker has a diameter of 0.447 m. (a) Assuming that the speed of sound is 343 m/s, find the diffraction angle θ for a 2.63-kHz tone. (b) What speaker diameter D should be used to generate a 5.83-kHz tone whose diffraction angle is as wide as that for the 2.63-kHz tone in part (a) ?

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  1. 15 September, 23:04
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    a) 20.78°

    b) 0.20m

    Explanation:

    wavelength = v/f

    λ = 343 / 2.6 * 10³

    = 0.13m

    the diffraction angle for a 2.6kHz tone is

    θ = sin⁻¹ (1.22 * 0.13 / 0.447)

    θ = 20.78°

    b) wave length of 5.83kHz

    λ = v/f

    λ = 343 / 5.83 * 10³

    = 0.059m

    D = 1.22 λ/sinθ

    D = 1.22 (0.059) / sin20.78°

    = 0.20m
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