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(D) For interference fringes to be observed,the superposing waves must have the same frequency and a constant phase difference.$1$. Waves $(i)$ and $(

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$(i)$ and $(ii)$ as well as $(iii)$ and $(iv)$

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(D) For interference fringes to be observed,the superposing waves must have the same frequency and a constant phase difference.$1$. Waves $(i)$ and $(ii)$ have the same angular frequency $\omega$. Thus,they can produce interference.$2$. Waves $(iii)$ and $(iv)$ have the same angular frequency $2\omega$. Thus,they can also produce interference.Therefore,interference fringes can be observed due to the superposition of $(i)$ and $(ii)$ or $(iii)$ and $(iv)$.

Four light waves are represented by:
$(i)$ $y = a_1 \sin \omega t$
(ii) $y = a_2 \sin (\omega t + \phi)$
(iii) $y = a_1 \sin 2\omega t$
(iv) $y = a_2 \sin 2(\omega t + \phi)$
Interference fringes may be observed due to the superposition of:

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Four light waves are represented by:$(i)$ $y = a_1 \sin \omega t$(ii) $y = a_2 \sin (\omega t + \phi)$(iii) $y = a_1 \sin 2\omega t$(iv) $y = a_2 \sin 2(\omega t + \phi)$Interference fringes may be observed due to the superposition of: