Low-lying electronic states of very long linear conjugated molecules with equal CC bond lengths is studied within the framework of Pariser and Parr's π electron approximation, by means of Tomonaga's one-dimensional sound wave method. It is found that as the number N of carbon atoms increases, the frequency of the sound wave with the lowest wave number tends to zero in proportion to √log N/N. It is shown that Araki and Murai's treatment which gives a result contradicting with ours contains a difficulty.