A) 3 and 4
B) 1 and 2
C) 2 and 3
D) 1 and 4
Correct Answer: D
Solution :
To see interference, we need two sources with the same frequency and with a constant phase difference. In the given waves, \[{{X}_{1}}={{a}_{1}}\,\sin \,\omega t\] and \[{{X}_{4}}={{a}_{1}}\,\sin \,(\omega t+\delta )\] have a constant phase difference \[\delta ,\] so interference is possible between them. For \[{{X}_{1}}={{a}_{1}}\,\,\sin \,\,\omega t,\] and \[{{X}_{2}}={{a}_{2}}\,\,\sin \,2\omega t,\] frequency is not equal and there is no constant phase difference. For \[{{X}_{1}}={{a}_{1}}\,\sin \,\,\omega t,\] and \[{{X}_{3}}={{a}_{1}}\,\sin \,\,{{\omega }_{1}}t,\] frequency is different and there is no constant phase difference.
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