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A sound wave is transmitted into a tube ...

A sound wave is transmitted into a tube as shown in figure. The sound wave splits into two waves at the point A which recombine at point B. Let R be the radius of the semicircle which is varied until the first minimu. Calculate the radius of the semi-circle if the wavelenght of the sound is `50.0 m`

Text Solution

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The sound travelling in the curved path distance = `pi R`
`L_(1) = pi R`
The sound travelling in the straight path distance = 2 R

The path distance of straight and curved path `DeltaP = L_(1) - L_(2) " " …… (1)`
The different in the path length of the sound waves ,
`Delta P = (lambda)/(2) " " .... (2)`
Equating (1) and (2) , `(lambda)/(2) = R(pi - 2) , lambda = 50 m`
`R = (lambda)/(2 (pi - 2)) = (50)/(2 (3.14 - 2)) = (50)/(2.28)`
`R = 21.9` m
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