For light waves are represented by 

(i) $y=a_1\sin \omega t$

(ii) $y=a_2\sin \left(\omega t+\varphi \right)$

(iii) $y=a_1\sin 2\omega t$

(iv) $y=a_2\sin 2\left(\omega t+\varphi \right)$

Interference fringes may be observed due to superimposition of