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

A = 14.45°

Step-by-step explanation:

given,

Frequency of sound = 1220 Hz

width of doorway = 1.13 m

speed of sound = 344 m/s

minimum angle = ?

Wavelength =
`(v)/(f)`

=
`(344)/(1220)`

= 0.28196 m

using formula

d Sin A = w

`sin A = (w)/(d)`

`sin A = (0.28196)/(1.13)`

`A = sin^(-1)(0.2495)`

A = 14.45°

So, the minimum angle relative to center line is equal to A = 14.45°