Two coherent narrow slits emitting sound of wavelength lamda in the same phase are placed parallel to each other at a small separation of 2lamda. The sound is detected by moving a detector on the screen sum at a distance D(gtgtlamda) from the slit S_1 as shown in figure. Find the distance x such that the intensity at P is equal to the intensity at O.

Two coherent narrow slits emitting sound of wavelength lamda in the sa

1.	Two coherent narrow slits emitting sound of wavelength lamda in the same phase are placed parallel to each other at a small separation of 2lamda. The sound is detected by moving a detector on the screen sum at a distance D(gtgtlamda) from the slit S_1 as shown in figure. Find the distance x such that the intensity at P is equal to the intensity at O.
Answer» Solution :Since `S_1, S_2` are in same phase at O there WIL be MAXIMUM intensity. Given that there will be a maximum intensity at P. `RARR path difference =/_\x=nl` From the ure (in question) `(S_1P)^2-(S_2P)^2` =(sqrtD^2+x_2)^2-[(sqrtD-2lamda^2+x^2]^2` `=4lamdaD=4lamda^2=4lamdaD` `(lamda^2` is so small and can neglected ) `S_1P-S_2P=(4lamdaD)/(2sqrt(x^2+D^2))=nlamda` `=(2D)/(sqrt(x^2+D^2))=n` `rarr n^2(x^2+D^2)=4D^2` `rarr x=D/n sqrt4-n^2` When `n=1, x=sqrt3D(1st order)` n=2, `x=0 (2ND order) `:.Wen x=sqrt3D` at P there will be maximum intensity