At which angles relative to the centerline perpendicular to the doorway will someone outside the room hear no sound? Use 344 m/sm/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.

Angle = 0.2520 radians

Explanation:

Complete 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.

Given Data:

Speed of sound =v= 344 m/sec    ;

Width of doorway =d= 1.13m          ;

Frequency of sound =f= 1220 Hz  ;

Solution:

As we know that

Wvelength = w = v/f = 344/1220 = 0.281967m

Now we also know that

w = dsin(A)      where A is the angle

A = arcsin(w/d) =14.44° = 14.44*(3.14/180) = 0.2520 radians

At the angle of 0.252 radians relative to the centreline perpendicular to the doorway a person outside the room will hear no sound under given conditions.