Explanation

(d) 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.