Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s

Question

Akira

Physics

28 January, 18:53

Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 5.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 1.00 m parallel to the wall, she experiences destructive interference for the first time. What is the frequency of the sound? The speed of sound in air is 343 m/s

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Eli Grant · Answer 1

This is a case of interference of sound, akin to YDSE in optics.

Here, like interference dark and bright fringes, region of silence and intense sound will be formed due to destructive and constructive interference respectively.

Here d = distance between two sources = 5 m

D = distance of source and screen = 12m

position of first destructive interference

= λ D / 2d

1 = λ 12 / 2x 5

λ = 5 / 6 m

frequency = v / λ

= 343 x 6 / 5

= 411.6 Hz