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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

Verified by Experts

Given
`lambda=50 m`
To find `R= ??`
Path difference `=piR-2R`
[ Here AB=2R, Semicircle path `pi=R]`

Formula :
Path formula `=(2pi-1)(lambda)/(2)` (for minimu n=1)
`R(pi-2)=(lambda)/(2)`
`:.R=(lambda)/(2(pi-2))`
`(50)/(2[(22)/(7)-2])=(50)/(2[(22-14)/(7)])`
`=(50xx7)/(2xx8)=27.875`
`=21.9 m`
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