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A) At the center, the path travelled by the sounds waves from the two speakers will be the same
==> No path difference.
Since the two waves were initialy in phase, the phase difference between the two waves for the
observer at center will be zero (additional phase difference = 2 x pi x path
difference/wavelength).
B) Now suppose the observer mooved towards one of detectors by a distance d, then the path
difference between the two waves will be 2d (as one has to travel d more and the other has to
travel d less)
==> for destructive interference, phase difference = 2 x pi x path difference/wavelength = pi
path difference = 2d ; wavelength = speed of sound / frequency = 343/(171.5) = 2m
==> d= wavelength/4 ; = 2/4 = 0.5 m = 50 cm
Solution
A) At the center, the path travelled by the sounds waves from the two speakers will be the same
==> No path difference.
Since the two waves were initialy in phase, the phase difference between the two waves for the
observer at center will be zero (additional phase difference = 2 x pi x path
difference/wavelength).
B) Now suppose the observer mooved towards one of detectors by a distance d, then the path
difference between the two waves will be 2d (as one has to travel d more and the other has to
travel d less)
==> for destructive interference, phase difference = 2 x pi x path difference/wavelength = pi
path difference = 2d ; wavelength = speed of sound / frequency = 343/(171.5) = 2m
==> d= wavelength/4 ; = 2/4 = 0.5 m = 50 cm

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A) At the center, the path travelled by the sounds waves from the tw.pdf

  • 1. A) At the center, the path travelled by the sounds waves from the two speakers will be the same ==> No path difference. Since the two waves were initialy in phase, the phase difference between the two waves for the observer at center will be zero (additional phase difference = 2 x pi x path difference/wavelength). B) Now suppose the observer mooved towards one of detectors by a distance d, then the path difference between the two waves will be 2d (as one has to travel d more and the other has to travel d less) ==> for destructive interference, phase difference = 2 x pi x path difference/wavelength = pi path difference = 2d ; wavelength = speed of sound / frequency = 343/(171.5) = 2m ==> d= wavelength/4 ; = 2/4 = 0.5 m = 50 cm Solution A) At the center, the path travelled by the sounds waves from the two speakers will be the same ==> No path difference. Since the two waves were initialy in phase, the phase difference between the two waves for the observer at center will be zero (additional phase difference = 2 x pi x path difference/wavelength). B) Now suppose the observer mooved towards one of detectors by a distance d, then the path difference between the two waves will be 2d (as one has to travel d more and the other has to travel d less) ==> for destructive interference, phase difference = 2 x pi x path difference/wavelength = pi path difference = 2d ; wavelength = speed of sound / frequency = 343/(171.5) = 2m ==> d= wavelength/4 ; = 2/4 = 0.5 m = 50 cm