What should be the diameter of the circular opening in a speaker?

Diffraction angle is 75

Speed of sound in air is 343 m/s If sin(diffracted angle) = 1.22( wavelength /diameter)

Wavelength = speed / frequency

This gives: Wavelength = 343/9100 = 0.0377m

Then: Diameter = 1.22 ( wavelength )/ sin(diffracted angle)

This gives: Diameter = 0.048 m

If we treat the
speaker like a simple circular aperture then there will be a diffracted angle of 75^{o} on
EACH side of the centre line. This gives a TOTAL SPREAD of 150^{o}. If the question
means a TOTAL spread of 75^{o} then the answer will be different.

Anyway –
assuming that it is 75^{o} EACH side of the centre line then, using the standard formula
for the diffraction at a circular opening:

Diameter of speaker x sin (diffracted angle)
=1.22 x wavelength

So: Diameter of speaker = 1.22 x Speed of sound/[frequency x
sin(diffracted angle)]

= 1.22 x 343/[9100xsin(75)]

= 1.22 x 343/[8790]

= 1.22 x 0.039

= 0.48 m

As you can see from the calculation if we had used the formula for a single
SLIT and not a CIRCULAR aperture we would have got 0.039m