Aspeaker 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

Explanation:

As we know by the law of diffraction through circular aperture

here we know that

a = diameter of the aperture

= diffraction angle

= wavelength

now we have

Now in order to find the wavelength we know

now we have

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explanation:

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .