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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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Olajidey

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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