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

A sound wave is transmitted into a tube as shown in figure. The sound

1.	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
Answer» <P> Solution :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 thesound 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