- #1
jemstone
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Wave Optics!
Sound with frequency 1240 Hz leaves a room through a doorway with a width of 1.19 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.
λf = v
θ = (m+.5)λ / d (because no sound is heard and therefore it's destructive?)
First I use the first equation to find λ. v/f = λ and therefore 344 m/s / 1240 Hz = .277419 m
Then I set m = 0 and used the second equation to find the angle:
θ = (m+.5)λ / d
θ = (.5 * .277419) / 1.19 m
I found that the angle was .1165 radians, but I know this is wrong. Help!
Homework Statement
Sound with frequency 1240 Hz leaves a room through a doorway with a width of 1.19 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.
Homework Equations
λf = v
θ = (m+.5)λ / d (because no sound is heard and therefore it's destructive?)
The Attempt at a Solution
First I use the first equation to find λ. v/f = λ and therefore 344 m/s / 1240 Hz = .277419 m
Then I set m = 0 and used the second equation to find the angle:
θ = (m+.5)λ / d
θ = (.5 * .277419) / 1.19 m
I found that the angle was .1165 radians, but I know this is wrong. Help!
