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Question
A sound wave is transmitted into a tube as shown in the figure. The sound wave splits into two waves at point A which recombine at point B. Let R be the radius of the semi-circle which is varied until the first minimum. Calculate the radius of the semi-circle if the wavelength of the sound is 50.0 m.
Solution
Given: λ = 50m
To find: R = ??
Path difference = πR – 2R
[Here AB = 2R; Semicircle path = πR]
Formula:
Path difference = (2n – 1)\[\frac{λ}{2}\] (for minimum n -1)
R(π - 2) = \[\frac{\lambda}{2}\]
∴ R = `lambda/(2(pi - 2))`
`= 50/(2[22/7 - 2])`
`= 50/(2[(22- 14)/7])`
`= (50 xx 7)/(2 xx 8)`
= 21.875
= 21.9 m
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