Falling interest rates: experts see outline of long-term economic relief taking shape.

Interest rates are tumbling along with economic activity - and the financial community is excited. ''The bandwagon effect is here now,'' says W. Lee Hoskins, chief economist at Pittsburgh National Bank.

Many money market experts now foresee a drop soon in the prime rate, the interest commercial banks charge their most creditworthy customers, from 17 or 17.5 percent to 16.5 percent. Mr. Hoskins predicts the prime will be down to 16 percent by year end and 14.5 or 15 percent by March or April of 1982.

H. Erich Heinemann, an economist with the investment banking firm of Morgan Stanley, forecasts the Federal Funds rate (the interest commercial banks charge each other on overnight loans to cover reserve shortages) will drop to 7.5 to 8. 5 percent next year from 13 to 13.5 percent currently. Interest on 30-year Treasury bonds could decline to 10.5 to 11.5 percent from today's 13.5 percent, he figures.

''There certainly has been an emotional shift in sentiment,'' noted Mr. Heinemann.

Such rate declines also mean lower interest charges on loans of immediate concern to consumers, such as those on mortgages, auto loans and personal loans. This will be vital to the housing and auto industries, both hard hit by high interest rates.

But both Hoskins and Heinemann caution that the speed of the interest rate decline may not be precipitous. Heinemann doesn't count on a straight line decline, but rather bumps along the route downward. ''I don't think there is a decisive point where all the problems are solved and rates settle to a single digit level.''

Many economists expect the Federal Reserve System to encourage the interest rate drop by once more lowering its discount interest rate, the fee it charges on loans to banks and other institutions. Last week that rate was cut from 14 to 13 percent, and it could soon be reduced to 12 percent.

The Fed, the experts say, now has plenty of room for such a maneuver within its targets for growth in the money supply, the fuel which feeds the fires of economic activity.

Says Heinemann: ''The Fed has regained control of the bank reserve numbers by all measures.'' A few weeks ago, Heinemann was concerned about the rapid growth of those commercial bank reserves because these are used by the banks to make loans, and thereby create new money. If the Fed was seen as giving up on its anti-inflationary monetary policy, interest rates would once more push skyward as lenders figured on higher inflation in the future. But the various measures of monetary growth show continued Fed restraint. The money supply measure known as M1-B fell $3 billion during the latest statistical week. So interest rates have fallen.

Hoskins points out that contrary to current Wall Street mythology, ''changes in the size of the federal deficit over time do not appear to be systematically related to interest rate movements.'' In other words, big deficits don't automatically mean high interest rates.

However, interest rates do tend to vary according to inflation rate expectations.

''The theory, in simple terms, is that lenders require a return sufficient to protect the purchasing power of the principal (the inflation premium) plus something for foregoing current consumption (the real return) in order to induce them to lend.''

Investors have learned that high rates of growth in the money supply produce higher inflation a year or two in the future, or vice versa. So, with money growing more slowly, they now figure they will need less of an inflation premium.

In addition, the slump in the economy has simply reduced the demand for money as businessmen strive to reduce the level of bank-financed inventories and other financing needs.

But will interest rates once more climb to new highs once the economy recovers, as some Wall Street analysts have predicted? They expect a large federal deficit and increased private demand for money to produce a credit crunch.

Hoskins disagrees with this scenario - as long as the Fed sticks to its money supply targets. If the Fed does try to end the recession by pumping up the money supply again, as it has done in previous slowdowns, ''then we are off to the races again'' with inflation and interest rates turning up, he says.

But Hoskins rather counts on the Fed remaining tough. He does not expect it to ''monetize'' large chunks of government debt, action that would pump up the money supply and eventually the inflation rate. The stern policy could prompt a brief upward movement of perhaps 1 percent in interest rates when the economy starts to expand again. But as market expectations of future inflation moderate, the upward bounce would be followed by a long-term decline in interest rates as inflation continues to move downward.

Hoskins has some suggestions to remove any market uncertainty about the Fed's tight money intentions:

First, he says, President Reagan should appoint individuals, be they bankers, businessmen, or economists, with strong views on monetary control to replace the retiring president of the Federal Reserve Bank of Cleveland and the retiring vice-chairman of the Fed's board of governors. Both are members of the Fed's policymaking Open Market Committee. Second, the Reagan administration needs to give full support to a slow money growth policy. Third, Congress must demonstrate some leadership by replacing election year policies with a continuous effort to trim the rate of growth in government expenditures.