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)

Question

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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Kiệt Gia 5 months 2021-09-05T11:32:05+00:00 1 Answers 0 views 0

Answers ( )

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    2021-09-05T11:33:20+00:00

    Answer:

    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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