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I have no idea how to determine the substituents on the aromatic ring from this NMR spectra. There is (or ‘might be’) a triplet on my NMR around $7.59 - 7.65\,\mathrm{ppm}$ which has 4 hydrogens in the same environment. If so, there must be two ortho substituents on two aromatic rings but I think the 4 Hs won’t be in the same environment.

I assume the substance to be the one I added here

enter image description here

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    $\begingroup$ Welcome to Chemistry.se! Are you sure that the compound you have drawn corresponds to the spectrum you have obtained? There are two singlets. At 3.86 it corresponds to the methoxy group. I see nothing in the molecule that might correspond to the 1.56 signal. (Maybe it is just water?) All the signals in your aromatic range have little shoulders (there are no values picked in this spectrum), but you should be able to calculate the coupling constants, with that information you might be able to correspond them to the protons in you compound. In principle, you should not see any triplet. $\endgroup$ – Martin - マーチン Mar 23 '15 at 6:29
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The hydrogens in the structure you drew definitely should not be in the same environment — so while overlapping or close signals would be okay, the way your signals look isn’t. To get two signals to be identical, there needs to be some symmetrical way of corresponding the hydrogens to each other.

I can confirm a trans-configured double bond (I assume you can, too?) and two disubstituted aromatic rings. The question remains which type of substitution they have (ortho, meta or para). If you expect two rings with the substituents you drew, remember they must be pretty different in their chemical shifts!

For ortho, as you drew, one would indeed expect a set of doublet, triplet, triplet, doublet for each ring. meta would expect one set of doublet, triplet, doublet and a singlet somewhere. para, finally, would expect two doublets.

Remember that triplets must have a $1\,:\,2\,:\,1$ ratio, or they aren’t triplets. With this information in hand, go back into the aromatic region and think what you could have gotten. I have dropped enough clues, I hope.

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