Sound with frequency 1240 Hz leaves a room through a doorway with a width of 1.13 m. At what minimum angle relative to the centerline perpendicular to the doorway will someone outside the room hear no sound? Use 344 m/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. Express your answer in radians.

Given Information:

frequency = 1240 Hz

width = a = 1.13 m

speed of sound = c = 344 m/s

Required Information:

angle = θ = ?

Answer:

θ = 14.18 rad

Explanation:

We can find out the angle relative to the centerline perpendicular to the doorway by using the following relation

sin (θ) = λ/a

Where λ is the wavelength of the sound wave and a is width

λ = c/f

Where c is the speed of the sound and f is the frequency

λ = 344/1240

λ = 0.277

sin (θ) = λ/a

θ = sin⁻¹ (λ/a)

θ = sin⁻¹ (0.277/1.13)

θ = sin⁻¹ (0.277/1.13)

θ = 14.18 rad