Question

Part complete Sound with frequency 1240 Hz leaves a room through a doorway with a width of 1.11 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.

Answer 1

14.43° or 0.25184 rad

Step-by-step 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

`\lambda=(v)/(f)\\\Rightarrow \lambda=(343)/(1240)\\\Rightarrow \lambda=0.2766\ m`

In the case of Fraunhofer diffraction we have the relation

`dsin\theta=\lambda\\\Rightarrow \theta=sin^(-1)(\lambda)/(d)\\\Rightarrow \theta=sin^(-1)(0.2766)/(1.11)\\\Rightarrow \theta=14.43^(\circ)\ or\ 0.25184\ rad`

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