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ANSWER:
Doorway Diffraction
Description: Use Fraunhofer diffraction to calculate the angle within which a person would not hear a sound from a room as it passes through
a door.
Part A
The width would increase.
The width would decrease.
The width would not change.
Sound with frequency 1280 leaves a room through a doorway with a width of 1.18 . At what minimum angle relative to the centerline
perpendicular to the doorway will someone outside the room hear no sound? Use 344 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.
Hint 1. How to approach the problem
For diffraction patterns in light there are a number of dark fringes in which waves of light completely cancel each other. For sound
waves this cancellation corresponds to silent spots at certain angles.
In this problem, we would like to know the angle at which the sound is completely canceled out. In order to determine this angle, we
first need to find the wavelength of the sound wave. This can be determined from the speed of sound and the frequency. You can then
determine the angle to the first destructive diffraction point from the standard Fraunhofer diffraction equation.
Hint 2. The equation for "dark" fringes
For single-slit Fraunhofer diffraction, the equation that relates the angle between subsequent dark (in this case silent) fringes and the
centerline to the wavelength of the incoming sound wave is
where is the wavelength of the sound, is the width of the diffracting slit, and is the angle between the th dark fringe and the
centerline of the image (see the figure).
Hint 3. Find the wavelength of the sound wave
Calculate the wavelength of the sound wave.
Express your answer in meters.
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