Mach number

(noun)

The ratio of the velocity of a body to that of sound in the surrounding medium.

Related Terms

  • doppler effect
  • sonic boom

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:
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