Figure shows two coherent sources S_1 and S_2which emit sound of wavelength lamda in phase. The separation between the sources is 3lamda. A circular wire at large radius is placed in such a way that S_1 S_2 lies in its plane and the middle point of S_1 S_2, is at the centre of the wire. Find the angular positions 0 on the wire for which constructive interference takes place.

Figure shows two coherent sources S_1 and S_2which emit sound of wavel

1.	Figure shows two coherent sources S_1 and S_2which emit sound of wavelength lamda in phase. The separation between the sources is 3lamda. A circular wire at large radius is placed in such a way that S_1 S_2 lies in its plane and the middle point of S_1 S_2, is at the centre of the wire. Find the angular positions 0 on the wire for which constructive interference takes place.
Answer» Solution :As shown in the URE `(S_1P)^2=(S_1x)^2+(Px)^`………1 `(S_2P)^2=(S_2M)^2+(PM)^2`……..2 from 1 and 2 `(S_1P)^2-(S_2P)^2=(Px)^2-(PM)^2` `=(1.5lamda+Rcostheta)^2-(Rcostheta-1.5lamda)^2` `=6lamdacostheta` `rarr (S_1P-S_2P)^2=(6lamdaRcostheta)/(2R)` `=3costheta` For constructive interferene `(S_1P-S-2P)^2=x=3lamdacostheta=nlamda` `rarr costheta=n/3` `theta=cos^-1(n/3)` `where n=0,1,2,.............. `rarr theta=0^@, 48^@, 2^@, 7^@, 5^@, 90^@ and` SIMILAR POINTS in other QUADRANTS.