Sound with frequency 1300 Hz leaves a room through a doorway with a width of 1.03 m. At what minimum angle relative to the centerline perpendicular to the doorway will someone outside the room hear no sound

Question

Francesca Chang

Physics

29 November, 15:12

Sound with frequency 1300 Hz leaves a room through a doorway with a width of 1.03 m. At what minimum angle relative to the centerline perpendicular to the doorway will someone outside the room hear no sound

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Answers (1)

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Brenden · Answer 1

about 14.7°

Explanation:

The formula for the angle of the first minimum is ...

sin (θ) = λ/a

where θ is the angle relative to the door centerline, λ is the wavelength of the sound, and "a" is the width of the door.

The wavelength of the sound is the speed of sound divided by the frequency:

λ = (340 m/s) / (1300 Hz) ≈ 0.261538 m

Then the angle of interest is ...

θ = arcsin (0.261538/1.03) ≈ 14.7°

At an angle of about 14.7°, someone outside the room will hear no sound.