Question

Sound with frequency 1220Hz leaves a room through a doorway with a width of 1.13m . At what minimum angle relative to the centerline perpendicular to the doorway will someone outside the room hear no sound? Use 344m/s for the speed of sound in air and assume that the source and listener are both far enough from the doorway for Fraunhofer diffraction to apply. You can ignore effects of reflections.

You can express it in either radians or degrees.

Answer 1

θ = 14.45º = 0.252 rad

Step-by-step explanation:

The expression that describes the phenomenon of diffraction is

a sin θ = m λ

Where a is the width of the exit opening in this case the width of the door, Lam is the wavelength, m the diffraction order for destructive interference,

Let's use the relationship between the speed of the wave is the producer of its frequency by the wavelength

v = λ f

λ = v / f

λ = 344/1220

λ = 0.282 m

sin θ = m λ / a

For the first destructive interference m = 1

sin θ = 1 0.282 /1.13

sin θ = 0.24956

θ = sin-1 (0.24956)

θ = 14.45º

We pass radians

θ = 14.45 (pi rad / 180º) = 0.252 rad