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

`a = 4.76 cm`

Step-by-step 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 = (1.22 \lambda)/(sin\theta)`

Now in order to find the wavelength we know

`\lambda = (c)/(f)`

`\lambda = (343)/(9100)`

`\lambda = 0.0376 m`

now we have

`a = (1.22(0.0376))/(sin75)`

`a = (0.046)/(0.966)`

`a = 0.0476 m= 4.76 cm`