A Wave is a Wave, by Angela Spivey -- Endeavors, Fall 1999

What do heartbeats, earthquakes, and whitecaps have in common?

A Wave is a Wave
by Angela Spivey

Your heart beats. Breakers crash against the shore. An earthquake rumbles. Do you feel the connection? It's a wave.

Though waves are common in nature, they aren't all that easy to measure or describe. For one thing, they're made of energy, not stuff you can see. Even when you're watching the ocean, you're not really seeing the waves—just their result, which is the movement of the water.

Whatever they're traveling around in, waves do have certain mathematically measurable components. Researchers can use these characteristics, such as frequency, amplitude, and velocity, to describe many types of waves.

The frequency of the heart's electrical waves, for example, may give researchers clues to the stability of the heart. The frequency tells you how fast the wave is oscillating—the number of times in one second that a crest, or high part, of the wave passes a fixed point. If a wave has a frequency of 10 hertz, for example, that means that in one second, 10 crests will pass.

A normal heart goes through a regular electrical sequence, which is what initiates its mechanical contraction, says Tim Johnson, associate professor of biomedical engineering. But that sequence is much more complicated than the tiny periodic blips that you see on an electrocardiogram (EKG) machine. The energy doesn't travel in simple pulses, but in a continuous wave.

"An EKG is just a composite signal measured in time," says Bonnie Punske, a former doctoral student at Carolina. Every fraction of a millisecond, voltage is measured, to create a signal that gives a general picture of heart performance.

For her doctoral dissertation, Punske made a more complicated measure of the heart. She treated cardiac activity as a wave and tracked it using a tiny sensor developed by The Biomedical Microsensors Laboratory at N.C. State University. Though it fits into the palm of your hand, the sensor has 144 tiny electrode sites, arranged in a 12-by-12 grid. The electrodes rest on the surface of the heart, and the sensor feeds measurements into a computer program that interprets them by performing mathematical calculations.

"During the time of one beat, we took the measurements from each electrode location every half millisecond," Punske says. "Then we treated the whole thing as one moving, propagating wave front."

One result was a range of frequencies for each wave. Since some parts of heart waves are oscillating faster than other parts, Punske's result wasn't a single number. "Instead of just one frequency, you'll have some fast components, some slow components—a spectrum of values of different frequencies that define the wave, that tell you something about each part of the wave," Punske says.

With these and other measurements, Punske, Johnson, and team hope to be able to predict when the heart's regular electrical sequence is about to be interrupted—an event called fibrillation. "Fibrillation is the electrical equivalent of the Tower of Babel," Johnson says. "It's like the heart's beating has lost all its organization." If fibrillation isn't corrected, then toxic chemicals build up, and the heart soon sustains damage.

The sensor allows the researchers to translate the heart's electrical waves into mathematical quantities that can be compared. The scientists hope to use their comparisons to find patterns, such as changes in direction or speed, that occur when the heart is about to fibrillate.

That's just the kind of information that geologists use when predicting earthquakes. By measuring electrical activity beneath the earth's surface, they know that, for instance, before an earthquake, the velocity of primary (P) waves decreases and then increases, returning almost to normal just before the earthquake happens.

No one thinks about that in North Carolina. But people started worrying when they felt a rumbling one day in September 1997. Rob Killough, a master's student in geology, has been studying this shaking event that occurred near Carolina's campus. He and other geologists still aren't sure what caused it.
Some people described the event as sounding and feeling like a big truck had hit their building. A few people on Franklin street reported that their car windows rattled.

A seismograph station near University Lake, the only station in the area, did indicate a disturbance. "Something had put a lot of energy into the ground," Killough says. "But the odd thing about it is that the event was relatively short in duration." Readings show that the seismic waves with the largest amplitudes, or crest heights, lasted a little over a second, Killough says. And the period after those largest waves, in which the waves are returning to normal, called the coda, was only about 21 seconds.

At first Killough thought that the event might have been a Lamb's pulse—a disturbance caused by a strong force hitting the ground—possibly a result of demolition at a nearby construction site. But the Chapel Hill event seems to have occurred at some depth, which rules out a Lamb's pulse.

After analyzing readings, Killough and other geologists are beginning to think that the event may have been a "microearthquake"—a disturbance whose magnitude registers below 2 or 3 on the Richter scale. The magnitude of the Chapel Hill disturbance appears to have been about 1.3. Geologists determine magnitude using different scales, but most involve measuring the amplitude of different types of waves, Killough says. One method, the moment magnitude, is determined from frequency measurements.

Geologists can also learn about an earthquake by measuring the velocity of its waves. Velocity measures how fast the wave front is traveling. To distinguish velocity from frequency, think of a snake moving across the ground. Its velocity would indicate how fast its head arrives at a destination; its frequency would be a measure of the rate at which its back is moving back and forth.

Wave velocity can be used to help determine an earthquake's epicenter, or point of origin. Geologists know that P waves travel faster than secondary (S) waves because P waves move more directly. P waves progagate in the same direction that the wave is traveling. One example is when two kids hold either end of a slinky, and one pushes an end toward the other, then pulls back to the original position. The resulting wave is a compression wave, or P wave. But S waves propagate perpendicular to the direction they're traveling. "So the ground could be oscillating side to side, while the disturbance is traveling forward," Killough says.

Since P waves travel faster, they always appear first on a seismogram, followed by S waves. Geologists measure how far apart, in seconds, these two waves appear at the measuring station. Because they know approximately how fast each kind of wave travels in a particular region, they can figure out with a simple calculation how far away from the recording station these waves began. "For instance, you can figure out how far away the epicenter had to have been for the P wave to take 20 seconds to get here, and the S wave to take 23 seconds," Killough says.

Killough has determined that the Chapel Hill disturbance's epicenter was somewhere near UNC Hospitals. But that's an estimate. Ideally, a geologist would calculate the epicenter using measurements from three different recording stations, using the intersection of the three points as the epicenter. But since there's only one local seismograph, Killough has had to make do with one set of measurements. "We'll probably never be one hundred percent sure what the event was," Killough says. "The best we can do is to narrow it down to a few possibilities."

Rob Turner also measures velocity and amplitude of waves, but a more
familiar type—those in the ocean. Turner, who recently completed his Ph.D. in marine sciences at Carolina, doesn't study waves for their own sake, but he measures them to determine their effect on erosion of beaches that are rimmed with beachrock, which is sand that has become cemented over time. Beachrock beaches are usually found in tropical or subtropical climates, such as Puerto Rico, where Turner did his work.

Turner uses electrical sensors to measure the motion of the water. "One sensor measures pressure, which can be translated into water depth," he says. "The higher the water pressure, the greater the depth. The rise and fall of water pressure reflects the passage of wave crests and troughs, respectively." Besides measuring waves, the sensors also measure current. Turner explains the difference between the two.

A wave isn't necessarily transferring the water from place to place—it's just making it a different shape. "There's just a circular motion of the water particles underneath the wave," he says. "You can feel it if you're standing in the ocean. You don't necessarily get driven into shore, but you just feel the water going up and down." Turner demonstrates a wave using an electrical cord. "Hold your end tight," he says. He jerks the other end, making a wave pass through the cord. "Now, my end of the cord didn't end up on your end; the matter itself didn't permanently change position. A wave—some energy—simply passed through it."

Unlike a wave, a current actually transports water from one place to another. That's what has happened when you're wading and suddenly find that you've somehow moved parallel to the shore, yards away from your towel.

There are also many more types of water waves than most people normally think of, Turner says. What most people think of as waves are what scientists call swell. They're waves with a period between crests of about eight to 12 seconds. "You'll actually see them come in and crash, come in and crash,"
Turner says.

Other waves you don't notice unless you watch the ocean for a while. These are lower frequency, bigger waves that have a period of about 50 to 100 seconds.

"Sometimes when you're standing on the beach, and the waves are sloshing back and forth, every once in a while, you'll have to run back because it was gonna get you," Turner says. "It's not that the wave that broke is any bigger. It's just that the crest of the low-frequency wave has come in." These low-frequency waves never really break, they just increase the overall depth of the water for a short period of time.

"There is no such thing in the ocean as one nice clean wave form," Turner says. There's a whole mixture of waves coming from different directions, and they add on to each other and subtract from each other."

The marine scientist, the seismologist, the cardiologist. They're all studying very different processes. But the lingo they use—frequency, amplitude, velocity—is often the same. Sometimes, what they're after isn't the stuff in which the wave travels. It's the energy coursing through it.

You do the Math

Whether it's seismic waves or ocean waves, one thing is required to measure them—math.

"To a mathematician, waves are functions which satisfy certain differential equations," says Mark Williams, professor of mathematics.

These equations express some physical law, such as Newton's second law, or laws of conservation of mass, momentum, or energy. A function is a mathematical rule that assigns to each element of one set of numbers (the domain) a single element of another set of numbers (the range).

To use a simple equation to describe a waveform, you have to think back to geometry class and how to graph a function. Such a function might look like this:

y = 4 - x²

Y indicates the position on the vertical axis of a graph, while x is the position on the horizontal axis.

To graph this function, plug in values for x to find y. For example,

if x = 0

then y = 4 - 0²

y = 4 - 0

y = 4

So you can plot these coordinates on the graph: (0,4).

Or, if x = 1

y = 4 - 1²

y = 4 - 1

y = 3

Now you can plot these coordinates: (1, 3). If you continue to plug in values for x, then solve for y, you'll end up with a graph that looks like the one below.