In the not-far future, supersonic passenger planes will criss-cross the world's oceans with unnerving frequency. Hundreds of flights a day, according to predictions, will shuttle business travelers from, say, Los Angeles to Tokyo and back before bedtime.

Will the sonic booms that accompany those flights pose problems for marine mammals?

Whales spend much of their time just below the ocean surface, rising frequently to breathe. Sonic booms, say existing estimates, can be heard at least a hundred feet down. But how loud is the noise a boom makes under water? Is it enough to spook a shallow-going whale? Enough to harm it?

The theory for calculating underwater sound pressure from sonic booms was developed over 25 years ago, says Judith Rochat, a graduate student in acoustics at Penn State. But that theory, Rochat adds, regards the ocean as a flat surface.

"What we're trying to develop is a more realistic model," she says. Rochat and her adviser, assistant professor of acoustics Victor Sparrow, envision a computerized model that will incorporate the sinusoidal troughs and crests of ocean waves, which can focus and diffuse sound. With this they hope to accurately predict how far sonic booms can dive.

Last year, as a first step, Sparrow used flat-ocean equations to predict the effect of aircraft speed on sound penetration. The faster the plane, he found, the deeper sound penetrates. The effect is minor near the surface, but increasingly significant at depths below 10 meters.

Sparrow was measuring peak sound pressures at given depths, Rochat notes; he didn't account for changes in sound as a boom goes deeper.

"A sonic boom in air," she explains, "takes the shape of an N-wave. It is impulsive -- sudden -- and it has a significant high-frequency component." When it penetrates water, the waveform changes: the N softens, and higher frequencies are lost.

Then there's the matter of how sound is perceived. Sparrow's calculated decibel levels, in this first go-round, were absolute measurements: unweighted. "An unweighted measurement," says Rochat, "is not good for determining annoyance."

As anyone knows who has blown on a dog whistle, the ear picks up certain frequencies better than others. In order to measure how a sound is actually heard, the more objective sound meter has to mask some frequencies and highlight others. "Weightings are a way to filter sound the way a human would hear it," Rochat says.

For a recent trial, she computerized five different sound-level measurements using three different weightings, each of which approximates human hearing a bit differently. Then she and Sparrow created a hypothetical SST with a speed of Mach 2.4 and a sonic boom of 300 milliseconds duration. They took simulated sound levels at eight depths underwater, weighted and unweighted.

At depths of tens of meters, the researchers found, unweighted sound levels dropped off ("decayed") hardly at all from their surface levels. Weighted levels, on the other hand, fell considerably. "Perceived noise levels may decrease rapidly with depth," Sparrow and Rochat write, "and the impact experienced may be significantly diminished compared with that predicted using unweighted levels."

"Of course," Rochat acknowledges, "all three of the weightings we used are based on the human ear. There aren't any weightings for marine mammals."

Even if noise descriptors are developed specifically for cetaceans, she adds, she and Sparrow will not attempt to determine what effects their predicted sound levels might have.

"Our job is just to get those levels. Determining the effects will be up to the marine biologists."

Judith Rochat is a doctoral student in the graduate program in acoustics, 217 Applied Research Laboratory, University Park, PA 16802; 814-865-6364. Victor W. Sparrow, Ph.D., is assistant profesor of acoustics, 157 Hammond Building, 865-3162. The research described above is funded by NASA.