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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Physics

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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Rylie Mckee · Answer 1

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