Question

A speaker is designed for wide dispersion for a high frequency sound. What should the diameter of the circular opening be in a speaker where the desired diffraction angle is 75° and a 9100 Hz sound is generated? The speed of sound is 343 m/s

Answer 1

Answer:

$a = 4.76 cm$

Explanation:

As we know by the law of diffraction through circular aperture

$a sin\theta = 1.22 \lambda$

here we know that

a = diameter of the aperture

$\theta$ = diffraction angle

$\lambda$ = wavelength

now we have

$a = \frac{1.22 \lambda}{sin\theta}$

Now in order to find the wavelength we know

$\lambda = \frac{c}{f}$

$\lambda = \frac{343}{9100}$

$\lambda = 0.0376 m$

now we have

$a = \frac{1.22(0.0376)}{sin75}$

$a = \frac{0.046}{0.966}$

$a = 0.0476 m= 4.76 cm$