Mach number

Examples of Mach number in the following topics:

• Speed of Sound

  • The general value given for the speed of sound is the speed of a sound wave in air, at sea level, at normal atmospheric pressure; that number is 344 m/s.
  • However, this number is not constant.
  • You may have heard the term Mach number in relation to speed of space craft or jets before.
  • The Mach number is given by the following, dimensionless equation:$M=\frac va$M - Mach numberv - Velocity of object a - Speed of sound in medium.
  • If something is travelling at the speed of sound, that would make the equation equal to 1, and can be denoted as Mach 1. shows a jet that is travelling at the speed of sound or faster.

• Non-relativistic Shocks

  • Let's define the Mach number of the incoming flow as $M_1=v_1/c_s$ and rewrite the fifth equation in this section as
  • As we take the limit of a stong shock $(p_2,V_2)$ we find that the compresssion ratio and square of the downstream Mach number approach
  • For $\gamma=5/3$ the compression ratio is 4 and the downstream Mach number is $1/\sqrt{5}$.
  • so the Mach numbers on each side of the shock are given by the ratio of the slope of the secant to the slope of the tangent.
  • As the shock decreases in intensity, the figure demonstrates that both Mach numbers approach unity.

• Application of Bernoulli's Equation: Pressure and Speed

  • This is determined by the dimensionless quantity known as the Mach number.
  • The Mach number represents the ratio of the speed of an object moving through a medium to the speed of sound in the medium.

• Sonic Booms

  • This is a critical speed, known as Mach.
  • The shock waves radiate out from the sound source, and create a "Mach cone' .
  • From previous atoms, we know that $\frac{v_s}{v_r}$is the sound source's Mach number.
  • The sound source has now broken through the sound speed barrier, and is traveling at 1.4 times the speed of sound, (Mach 1.4).

• Radiative Shocks

  • The initial and final Mach numbers and densities are related through

• Moving Source

  • However, now the sound source is moving to the right with a speed υs = 0.7 c (Mach 0.7).

• Moving Observer

  • However, now the sound source is moving to the right with a speed υs = 0.7 c (Mach 0.7).

• General Case

  • However, now the sound source is moving to the right with a speed υs = 0.7 c (Mach 0.7).

• Round-off Error

  • A round-off error is the difference between the calculated approximation of a number and its exact mathematical value.
  • Calculations rarely lead to whole numbers.
  • The number $\pi$ (pi) has infinitely many digits, but can be truncated to a rounded representation of as 3.14159265359.
  • However, when doing a series of calculations, numbers are rounded off at each subsequent step.
  • Rounding these numbers off to one decimal place or to the nearest whole number would change the answer to 5.7 and 6, respectively.

• Scientific Notation

  • Scientific notation is a way of writing numbers that are too big or too small in a convenient and standard form.
  • In scientific notation all numbers are written in the form of $a\cdot 10^{b}$  ($a$ multiplied by ten raised to the power of $b$), where the exponent $b$ is an integer, and the coefficient $a$ is any real number.
  • Each number is ten times bigger than the previous one.
  • Continuing on, we can write $10^{-1}$ to stand for 0.1, the number ten times smaller than $10^{0}$.
  • Negative exponents are used for small numbers: