The first of 15 noise monitoring devices to record the volume of the 600 commercial jets that fly in and out of National Airport each day have been set up in Rosslyn and near Fort Hunt and are scheduled to be in operation by tomorrow.

The remaining monitors are expected to go up within the next few weeks. All are being mounted on utility poles or buildings and will use telephone lines to send noise data to a computer at Dulles International Airport, where similar monitors were installed two years ago to listen to supersonic Concorde flights.

The noise levels are not expected to be made public on a daily basis until spring, when the $221,500 system is in full operation.

National's monitors will provide the first major test of the noise that residents living near the airport have complained about since commercial jets first began using National in 1966.

The Federal Aviation Administration, which operates Dulles and National, has never monitored the plane noise near its downtown airport, one of the dozen busiest airport in the world. However, it has prepared maps that estimate how loud certain types of jets might sound at different distances from the airport and from the center of the Potomac River, the theoretical flight path for all planes using. National. It concluded that those noise levels were tolerable.

A study by the Alexandria city health department, which has more than 12,000 residents living within four miles of National's main runways, found, however, that the majority of National's planes do not fly a center-of-the-river course but instead hug the city's shoreline. Although planes leaving National were directed by the FAA last summer to fly a center of the river course, many residents claim there has been no noticeable difference in flight patterns.

Alexandria also is the only local jurisdiction to conduct live noise tests of planes using National. The brief test, for part of one day in the summer of 1976, found that planes were twice as loud in the city as on the deserted Maryland shore opposite Alexandria and were unacceptably loud for a residential area.

The city will have one of the seven Virginia monitors on its waterfront. Fairfax County will have four monitors and Arlington will have two. Four will be in the District and two each in Montgomery and Prince George's counties.

Instant noise readings will be shown on display boards to be installed in National's main lobby, identifying airplanes and their noise levels as they pass each of the monitors. A similar display board is to be installed in the FAA's downtown deadquarters in L'Enfant Plaza.

Monthly reports showing noise levels of all planes at both airports will be issued, according to James T. Murphy, FAA's director of metropolitan Washington airports. In addition, when a resident calls to complain about a noisy plane flying nearby, the FAA and the caller will abable to identify the plane, the noise recorded at monitoring stations and even the craft's height and exact flight pattern.

The latter information will become available when the two airports' radar systems, which make videotape records of all plane flight patterns, also are fed into the computer. The new monitoring system, and the information it will make public, is expected to make airlines more responsible about the flight paths and noise of their airplanes.

"We hope to achieve a high level of compliance with noise abatement regulations by the airlines . . ." Murphy said in announcing the monitoring program last year.