Answer:
14.43° or 0.25184 rad
Explanation:
v = Speed of sound in air = 343 m/s
f = Frequency = 1240 Hz
d = Width in doorway = 1.11 m
Wavelength is given by
[tex]\lambda=\frac{v}{f}\\\Rightarrow \lambda=\frac{343}{1240}\\\Rightarrow \lambda=0.2766\ m[/tex]
In the case of Fraunhofer diffraction we have the relation
[tex]dsin\theta=\lambda\\\Rightarrow \theta=sin^{-1}\frac{\lambda}{d}\\\Rightarrow \theta=sin^{-1}\frac{0.2766}{1.11}\\\Rightarrow \theta=14.43^{\circ}\ or\ 0.25184\ rad[/tex]
The minimum angle relative to the center line perpendicular to the doorway will someone outside the room hear no sound is 14.43° or 0.25184 rad
