Answer:
about 14.7°
Explanation:
The formula for the angle of the first minimum is ...
sin(θ) = λ/a
where θ is the angle relative to the door centerline, λ is the wavelength of the sound, and "a" is the width of the door.
The wavelength of the sound is the speed of sound divided by the frequency:
λ = (340 m/s)/(1300 Hz) ≈ 0.261538 m
Then the angle of interest is ...
θ = arcsin(0.261538/1.03) ≈ 14.7°
At an angle of about 14.7°, someone outside the room will hear no sound.
