To solve this problem we will apply the concepts related to wavelength, as well as Rayleigh's Criterion or Optical resolution, the optical limit due to diffraction can be calculated empirically from the following relationship,
[tex]sin\theta = 1.22\frac{\lambda}{d}[/tex]
Here,
[tex]\lambda[/tex] = Wavelength
d= Diameter of aperture
[tex]\theta[/tex] = Angular resolution or diffraction angle
Our values are given as,
[tex]\theta = 11\°[/tex]
The frequency of the sound is [tex]f = 9100 Hz[/tex]
The speed of the sound is [tex]v = 343 m/s[/tex]
The wavelength of the sound is
[tex]\lambda = \frac{v}{f}[/tex]
Here,
v = Velocity of the wave
f = Frequency
Replacing,
[tex]\lambda = \frac{(343 m/s)}{(9100 Hz)}[/tex]
[tex]\lambda = 0.0377 m[/tex]
The diffraction condition is then,
[tex]sin\theta = 1.22\frac{\lambda}{d}[/tex]
Replacing,
[tex]sin(11\°) = 1.22\frac{(0.0377 m)}{(d)}[/tex]
d = 0.24 m
Therefore the diameter should be 0.24m
