16.9 - Supersonic speed and shock waves
After studying the Doppler effect equations, you might
wonder: What happens if the speed of the sound
source equals the speed of sound? The relevant
Doppler equation shows that you would have to divide
by zero, yielding infinite frequency, a troubling result.
Equally troubling was the result when aircraft first
tried to break the sound barrier (the speed of sound).
In the first half of the 20th century, the planes tended
to fall apart as much as the equation does. It was not
until 1947 that a plane was able to fly faster than the
speed of sound, as excitingly shown in the movie The
Right Stuff, proving that sound was not a barrier after
all.
The Doppler effect equations do not apply if the sound source is moving at or above the
speed of sound. Concept 1 shows the result when a sound source moves at the speed
of sound. The leading edges of the sound waves bunch up at the tip of the aircraft as
the plane travels as fast as its own sound waves.
Concept 2 shows the result when an aircraft exceeds the speed of sound. Aircraft
capable of flying that fast are called supersonic. The plane travels faster than its own
sound waves, and the waves spool out behind the plane creating a Mach cone.
The surface of the Mach cone is called a shock wave. Supersonic jets produce shock
waves, which in turn create sounds called sonic booms. As long as a jet exceeds the
speed of sound, it will create this sound. A rapid change in air pressure causes the
sonic boom. Shock waves may be visible to the human eye because a rapid pressure
decrease lowers temperature and causes water molecules to condense, resulting in fog.
You may have heard other sonic booms, such as the report of a rifle or the crack of a
well-snapped whip. The boom indicates that the bullet or the tip of the whip has moved
faster than the speed of sound. The example of the whip shows that the moving object
can be silent and still create a shock wave.
Equation 1 shows how the sine of the angle of a Mach cone can be calculated as a ratio
of speeds. The inverse ratio, of the speed of the object to the speed of sound, is known
as the Mach number. A fighter jet described as a “Mach 1.6 plane” can move as fast as
1.6 times the speed of sound, or about 550 m/s (more than 1200 mph). You see this
described mathematically in Equation 2. Because the speed of sound varies with factors
like temperature, the exact speed of a Mach 1.6 plane depends on its environment.
This boat is traveling faster than the speed of waves in water.
Its wake forms a two-dimensional "Mach cone" on the water's surface.When object is at speed of
sound
It travels as fast as its own sound waves
Supersonic speed
Object exceeds speed of its sound
waves
·Sound waves form Mach cone
·Surface of cone is shock wave
·Angleș is called Mach angle