A packed auditorium at the National Academy of Sciences last night clapped madly for every element of the ceremonial opening of "Egypt Today."

Jihan Sadat, wife of the Egyptian president, made a gracious half-hour speech in admirable English (her mother was an Englishwoman). She recently earned an advanced degree, her thesis being the influence of Shelley on Arabic literature.

This won, needless to say, the heart of Joseph Duffey, chairman of the National Endowment for the Humanities and a real buff for things on file, and Livingston Biddle, chairman of the National Endowment for the Arts, who quoted one of Shakespeare's celebrated songs ("Hark, hark the lark at heaven's gate sings") which he said he hoped was by Shelley, and which had an application to the "Egypt Today" show since Phoebus, in the song, is of course the Greek sun god and the Egyptian sun god, Amen-Ra, was somewhat similar. (And somewhat different.) Furthermore, there is a celebrated Egyptian temple at which the door is so situated that the first light of the rising sun and perhaps the lark also, penetrates to the sanctuary on the pharaoh's birthday, he said, and everyone felt he had made a pretty tribute to the glory of Egypt and clapped vigorously. He did not speak long. t

L. Dean Brown, president of the Middle East Institute; Charles Z. Wick, new director of the International Communication Agency; and S. Dillon Ripley, secretary of the Smithsonian Institution, all made short talks.

Wick, evidently meaning a compliment to Mrs. Sadat's beauty, said with a gallant nod in her direction that if all goverment heads were like her, there would be no problems.

"Egypt Today" involves numerous museum shows on aspects of ancient and modern Egypt, and a number of lectures and seminars running well into April. The two national endowments, private corporations and individuals contributed several hundred thousand dollars for the cultural festival and the Egyptian state bore many expenses in contributing exhibits.

After a spell the speakers left the dais and sat in auditorium seats, accompanied by Ashraf A. Ghorbal, ambassador of Egypt; Mamdouh Gabr, Egyptian minister of health; Joseph John Jova, president of Meridian International House; Janet W. Solinger, director of the Smithsonian Resident Associate Program; and John Dorman, project director for the whole shebang.

The Heifny Quintet played instrumental music which at first sounded like something mysterious and wicked on the other side of a beaded doorway in Cairo and then (as Western ears got tuned in a little) more impressive and serious. Few perhaps had ever heard a tambourine solo and judging by the applause, which threatened not to stop, everyone was pleased to be culturally broadened. The oud, the qanun, the nay, the el-rek and the violin were all impassioned, in perfect sympathy with each other, and played with obvious love and skill.

Fifteen dancers of the Reda Folkloric Troupe, in which the women were more beautiful than one expects or finds dancers to be, performed with high-style cabaret competence and the women wore shoes golder than gold leaf.

A reception followed, with canapes and sausages and pate, in the Roman-Byzantine hall of the academy, and to any late arrivals for the food it may have seemed like a Christmas Eve sale at Saks as the outer fringes formed one-man phalanxes in to the tables. In time, all were filled, especially after it was discovered coffee and pastries were in an adjoining room.

It was not much like Luxor, of course, but Egypt has come a long way.