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Jet sonic booms

Q: When a jet breaks the sound barrier does the boom only happen at that point or continue as long as the jet exceeds that speed? (Pete, Tucson, Arizona)

What happens when a plane goes faster than the speed of sound? (Omar, Kuwait)

A: The jet continues to form a shock wave and, therefore, a sonic boom as long as the jet plows through the air faster than sound. (It must go about 750 miles per hour (1210 km/h) in order for the boom to be heard on the ground.) A groundling, of course, only hears a sonic boom once as the shock wave passes her.

Off the coast of Pusan, South Korea: an FA-18 Hornet breaks the sound barrier. The unusual cloud is due to a drop in surrounding air pressure (as the shock wave formed) and a corresponding drop in temperature that caused air moisture to condense and make a cloud. [Courtesy of US Air Force and Wikipedia]

Sound waves and water waves are similar. So let’s consider water waves from a boat put in the water and moving on the surface in order to better understand sound waves and sonic booms in the air. As we’ll soon see, the sonic-boom shock wave is like a bow wave (and wake) of a moving boat.

We watch a boat and a jet:

First, the boatman puts the boat in the water. It pushes water molecules out of its way, which causes pressure waves to ripple outward. See Figure 2.

Looking down on a motorboat in a quiet lake. Little waves ripple outward. Drawing by the author.

Now he applies a little power and the boat moves slowly along the lake. It generates ripples but it also moves and displaces the center of the ripples in its direction of motion. See Figure 3, top picture.

The boat moving through the water slowly (top picture). The jet traveling subsonic and closing in on its sound waves (bottom picture).

Similarly, the jet moving overhead subsonically pushes air out of the way and, in so doing, generates pressure waves that move at the speed of sound. Moreover, the jet, like the slow boat, moves the center of its waves in its direction of motion. See Figure 3, bottom picture.

As the center of each boat ripple moves forward with the boat, the waves crowd up in front of the boat and stretch out behind. Similarly, the centers of sound waves move forward with the jet, bunch up in front of the jet, and spread further apart behind.

A bird ahead of the jet hears a higher frequency and, therefore, a higher pitch than a bird flying behind. This is called a Doppler effect and likewise explains the sudden change in pitch of a car horn when the car races by, says Daniel A. Russell, physics professor at Kettering University.

Meanwhile, the boatman throttles up and the boat surges ahead. When the boat exceeds the speed with which the ripple waves in front travel, the boat overtakes the waves. The overtaken waves form a bow wave — a single wave made up of all the ripple waves that would have propagated ahead of the boat but could not move fast enough to do so. See Figure 4, top picture.

The boat — moving faster than the spreading ripples — forms a 2-dimensional "V" bow wave (top picture). The jet exceeds the speed of sound (bottom picture) and overtakes the forward rippling sound waves that can’t "get out of the way." The overtaken sound waves form a 3-dimensional cone shock wave much like a bow wave of a surface boat.

Almost the same thing happens when the jet breaks the sound barrier. When the jet exceeds the speed of sound — the sound waves can’t get out of the way of the jet. So, they scrunch together and form a kind of "bow wave" that is called a shock wave — a sonic boom. The only difference is that the boat wave forms a 2-dimensional "V" on the water surface and the shock wave forms a 3-dimensional cone. See Figure 4.

The shock wave thus formed contains all of the sound energy packed into the wave front. As the front passes birds in the air and us on the ground, we hear a thump. The sonic boom lasts only about a tenth of a second for most military jets and up to a half second for the space shuttle or Concorde jetliner.

The lateral spread of a boom on the ground (the "wake" width) is about 30 miles (50 km) for a jet flying supersonic at 30,000 feet (9000 m).

Hearing a sonic boom is like being on a lakeshore and watching a boat speed by. As the boat passes, no special waves hit the shore. But a little while later, the bow wave hits the shore. It’s a big wave like a big sonic boom. And that wave continues to hit all along the shore as long as the boat exceeds the speed of its ripple waves and therefore forms a bow wave.

Likewise, the sonic boom persists, upsetting birds and people, as long as the plane continues to fly faster than sound travels.

Further Reading:

Kettering University: The Doppler effect and sonic booms by Daniel A. Russell

HyperPhysics: Speed of sound

Wikipedia: Sonic boom

SkyFlash.com: What is a sonic boom

NOVA: Sonic boom basics

(Answered Dec. 6, 2005)