Metro officials said yesterday they think they have found a solution to the irritating problem of the subway's screeching brakes.

Theodore Weigle, Metro's assistant general manger for transit services, made that announcement at the Metro board meeting. "I can't say for certain when" Metro's trains will stop shrieking when they stop, he said, "but a solution is close."

The short-term answer will be the refitting of Metro's 300 subway cars with 4,800 new brake pads, which will cost about $120,000. One set of the new pads has been installed on a two-car train, which has run quietly around the system at night. Four hundred more pads are on order so several trains can be fitted and tested. If the new pad works as it has on the test, it will be purchased and installed fleetwide as quickly as possible, Weigle said in an interview.

"We'll still get some squeal, but you can live with it, said Erich Vogel, the subway maintenance chief.

Weigle said that acoustical testing has found that the disc in the braking system acts like a bell (the pad is the clapper) for the high-pitched tone that has driven some riders from the subway and caused others to cover their ears whenever trains enter a station. At some point, the discs will have to be modified, he said. Discs cost $325 each, so a fleetwide replacement would total at least $780,000.

A program to modify the entire braking system is also receiving heavy study.

The board approved yesterday a public hearing required before Metro can apply for $2.3 million in federal funds to buy and test an advanced braking system.

There was othe good news yesterday for board members. Metro budget director Eckhard Bennewitz said that for the first time in six years, Metro will complete a fiscal year with a decrease in the budgeted subsidy required to operate both bus and subway systems.

Controls on overtime, hiring and manning levels plus a big fare increase Jan. 1 have made it possible, Bennewitz said. Total subsidy, including local, state and federal sources, was originally projected at $139.7 million. The midyear update projects a total subsidy of $135.9 million.

In other Metro matters yesterday:

The board's "Miracle Committee," which was supposed to resolve irreconcilable differences between Maryland, Virginia and the District on whether dollar bills should continue to be accepted on buses, disbanded after failing. The kill-the-dollar-bill issue was shelved indefinitely, some hope forever.

D.C. board member the Rev. Jerry A. Moore said the District is "deeply concerned with the failure of Fairfax County to pay its subsidy." The county, protesting Metro financial management, is $15.4 million in arrears in payments to the operating fund. Officials estimate that Metro will have to borrow by March 20 to operate if the county does not pay.

Moore noted that similar protests have occurred in the past, but added, "I don't remember that any of us have pouted so long . . . The decision has to be made whether other jurisdictions can bear the burden of providing transportation to jurisdictions that do not pay." Joseph Alexander, board member from Fairfax County, said he shared Moore's concern, but said he thought the issue would be resolved shortly. The Metro board took no action. t

The board was told that transit ridership during the last half of 1980 increased slightly over the preceding year, but at an average of 613,239 riders per weekday was a little lower than projected. Bus ridership has actually held steady although a decrease had been projected; rail ridership is slightly below projections. General Manager Richard S. Page attributed that to a big fare increase in July followed by publicity about possible service cuts and another increase; "some reliability problems with Metrorail service;" squealing brakes on the trains, and "possibly an overly optimistic estimate of ridership growth. . . ."

The board adopted a resolution supporting efforts in the Maryland and Virginia legislatures and in Congress to strip from law a requirement that unresolved labor contract issues at Metro be settled through binding arbitration. Metro management believes the requirement has resulted in continuing excessive quarterly salary adjustments for its transit workers, the fourth best paid per hour in the nation.

The board awarded a $234,703 contract to Geron Restoration Corp. to stop leaks in six underground subway stations -- Federal Triangle, Federal Center SW, Capitol South, Eastern Market, Potomac Avenue and Stadium-Armory. Those stations, on the combined Blue-Orange lines, have leaked from the day they opened in July 1977.