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Subsonic flight

Subsonic

Subsonic refers to speeds slower than the speed of sound.

When a source emits sound waves and is moving slower than the speed of sound you get the situation in this picture. Notice that the source moving means that the wavefronts, and therefore peaks in the wave, are actually closer together in the one direction and further apart in the other.

If you measure the waves on the side where the peaks are closer together you'll measure a different wavelength than on the other side of the source. This means that the noise from the source will sound different on the different sides. This is called the Doppler Effect .

Doppler Effect

when the wavelength and frequency measured by an observer are different to those emitted by the source due to movement of the source or observer.

Supersonic flight

Supersonic

Supersonic refers to speeds faster than the speed of sound.

If a plane flies at exactly the speed of sound then the waves that it emits in the direction it is flying won't be able to get away from the plane. It also means that the next sound wave emitted will be exactly on top of the previous one, look at this picture to see what the wavefronts would look like:

Sometimes we use the speed of sound as a reference to describe the speed of the object (aircraft in our discussion).

Mach Number

The Mach Number is the ratio of the speed of an object to the speed of sound in the surrounding medium.

Mach number is tells you how many times faster than sound the aircraft is moving.

  • Mach Number < 1 : aircraft moving slower than the speed of sound
  • Mach Number = 1 : aircraft moving at the speed of sound
  • Mach Number > 1 : aircraft moving faster than the speed of sound

To work out the Mach Number divide the speed of the aircraft by the speed of sound.

Mach Number = v aircraft v sound

Remember: the units must be the same before you divide.

If the aircraft is moving faster than the speed of sound then the wavefronts look like this:

If the source moves faster than the speed of sound, a cone of wave fronts is created. This is called a Mach cone. From constructive interference, we know that two peaks that add together form a larger peak. In a Mach cone many, many peaks add together to form a very large peak. This is a sound wave so the large peak is a very, very loud sound wave. This sounds like a huge "boom" and we call the noise a sonic boom .

Sonic Boom

A sonic boom is the sound heard by an observer as a shockwave passes.

An aircraft flies at 1300 km · h - 1 and the speed of sound in air is 340 m · s - 1 . What is the Mach Number of the aircraft?

  1. We know we are dealing with Mach Number. We are given the speed of sound in air, 340 m · s - 1 , and the speed of the aircraft, 1300 km · h - 1 . The speed of the aircraft is in different units to the speed of sound so we need to convert the units:

    1300 km · h - 1 = 1300 km · h - 1 1300 km · h - 1 = 1300 × 1000 m 3600 s 1300 km · h - 1 = 361 . 1 m · s - 1
  2. We know that there is a relationship between the Mach Number, the speed of sound and the speed of the aircraft:

    Mach Number = v aircraft v sound

    We can use this relationship to find the Mach Number.

  3. Mach Number = v a i r c r a f t v s o u n d Mach Number = 361 . 1 340 Mach Number = 1 . 06

    The Mach Number is 1.06.

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fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
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Graphene has a hexagonal structure
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Source:  OpenStax, Maths test. OpenStax CNX. Feb 09, 2011 Download for free at http://cnx.org/content/col11236/1.2
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