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.

Answer 1

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