Two waveforms, y1x,t=Asinkx−ωt and  y2x,t=Asinkx+ωt+π3, travelling along x- axis are superposed. The position of nodes is given byk=2πλ;  ω=2πf

Given y1(x,t)=Asin⁡(kx−ωt)….(1)y2(x,t)=Asin⁡kx+ωt+π3….(2) From principle of superpostion y=y1+y2y=Asin⁡(kx−ωt)+Asin⁡kx+ωt+π3∵sin⁡C+sin⁡D=2sin⁡C+D2⋅cos⁡C−D2=2Asin⁡kx+π6cos⁡ωt+π6 Nodes are given by kx+π6=nπkx+π6=nπ∵k=2πλ⇒2πxλ+π6=nπ⇒x=nπ−π6λ2π∴xn=n−16λ2