The Federal Aviation Administration has awarded a $221,500 contract to a California firm to install aircraft noise monitoring equipment this fall around National Airport.

Not all of the 13 or 14 monitoring sites have been selected, but at least one will be along Alexandria's waterfront, where residents of Old Town have complained for years about low-flying jets.

Purchase of the noise monitors is the first step of an FAA program that within a year will see illuminated boards at National Dulles Airports, showing noise levels of planes as they pass each monitor, and will allow instant computer feedback on how much noise each plane is making and exactly where it if flying.

The FAA has never done any noise monitoring near National Airport, although it has done theoretical studies based on the premise that planes fly over the middle of the Potomac River on approaches and departures.

City resident have complained, however, that jets do not fly over the center of the river - and still don't despite new FAA directives this summer. A city study last year found that 83 out of 100 planes leaving National hugged the water-front and that many actually flew over the edge of the city. Noise monitoring by city health officials found that National's jets made twice as much noise in Old Town, where 12,000 persons live within a few blocks of the river, than on the deserted Maryland shore opposite Alexandria.

Noise monitoring equipment was installed at Dulles last year to assess the impact the supersonic Concordes were making and was extended last Mary to cover all flights at Dulles. The new National Airport monitors, which will be attached to utility poles and buildings, will use telephone lines to send noise readings to Dulles, where a computer will ecord and analyze the readiungs from both airports, according to the FAA.

The large display boards will be erected early next year at both airports and at the FAA's downtown headquarters building.

In addition to three instantaneous readings, the computer next year will be programmed to issue monthly reports on the noise levels of all planes using the airports.

Coordinated with taped radar information, the computer will report the location, height, direction, speed and noise levels of every plane, and identify the flight number of every plane. This will take several days at first but by next fall "we should have immediately retrievable information so that when someone calls in with a noise complaint we'll be able to know instantly" the noise levels and location of the plane the caller is talking about, said James T. Murphy, the FAA's director of metropolitan Washington airport.

Once the FAA and the public has that kind of information, Murphy said, "We hope to achieve a high level of compliance with noise abatement regulations by the airlines, although safety first will always be the major factor."